PSC Notes

Earthquakes

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Earthquakes occur when energy stored in elastically strained rocks is suddenly released. This release of energy causes intense ground shaking in the area near the source of the earthquake and sends waves of elastic energy, called seismic waves, throughout the Earth. Earthquakes can be generated by bomb blasts, volcanic eruptions, sudden volume changes in minerals, and sudden slippage along faults. Earthquakes are definitely a geologic hazard for those living in earthquake prone areas, but the seismic waves generated by earthquakes are invaluable for studying the interior of the Earth.

The point within the earth where the fault rupture starts is called the focus or hypocenter. This is the exact location within the earth were seismic waves are generated by sudden release of stored elastic energy.

The epicenter is the point on the surface of the earth directly above the focus. Sometimes the media get these two terms confused.

Seismic waves are the vibrations from earthquakes that travel through the Earth; they are recorded on instruments called seismographs. Seismographs record a zig-zag trace that shows the varying amplitude of ground oscillations beneath the instrument. Sensitive seismographs, which greatly magnify these ground motions, can detect strong earthquakes from sources anywhere in the world. The time, locations, and magnitude of an earthquake can be determined from the data recorded by seismograph stations.

 

Two of the most common methods used to measure earthquakes are the Richter scale and the moment magnitude scale.

The Richter scale is used to rate the magnitude of an earthquake, that is the amount of energy released during an earthquake.
The Richter scale doesn’t measure quake damage (which is done by Mercalli Scale) which is dependent on a variety of factors including population at the epicentre, terrain, depth, etc. An earthquake in a densely populated area which results in many deaths and considerable damage may have the same magnitude as a shock in a remote area that does nothing more than frightening the wildlife. Large-magnitude earthquakes that occur beneath the oceans may not even be felt by humans. Richter Scale of Earthquake Energy
The magnitude of an earthquake is determined using information gathered by a seismograph.
The Richter magnitude involves measuring the amplitude (height) of the largest recorded wave at a specific distance from the seismic source. Adjustments are included for the variation in the distance between the various seismographs and the epicentre of the earthquakes.
The Richter scale is a base-10 logarithmic scale, meaning that each order of magnitude is 10 times more intensive than the last one.

 

Parliamentary Form of Government

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Parliamentary form of Government is the system of government in which there exists an intimate and harmonious relationship between the executive and the legislative departments, and the stability and efficacy of the executive department depend on the legislature.Its a system of government in which the power to make and execute laws is held by a parliament.

Although the parliamentary government is broadly defined in the above way, in such a system the supremacy of the legislature has now been replaced by the supremacy of the Cabinet. Hence, such form of government is also called Cabinet Government.

In a Parliamentary form of government, the head of the state is usually a different person than the head of the government. A Monarch or a President is usually the head of the state. However, he or she is the head of state, but not the head of government. The functions of the head of the state is chiefly formal or ceremonial. The council of ministers or the cabinet exercises the real executive powers and authority to run the Government. In many countries, the Prime Minister is the the head of the council of ministers.

The Parliamentary or the Cabinet system originated in England. This form of government exists in countries like Britain, India and Canada. This Parliamentary form of government is also called Responsible government.

Features

 

The features of Parliamentary form of Government has been discussed below:

 

  1. Existence of a Titular or Constitutional Ruler: The first characteristic feature of the parliamentary system is the existence of a Titular of Constitutional Ruler. Legally the administration of all the affairs of the state is conducted by the head of the state. In reality, however, the administration is carried by the Council of Ministers. The Monarch or the President, as the case may be, is the head of the state, but not the head of the government.

 

  1. Absence of Separation of Powers: In the parliamentary system the principle of separation of powers is not adopted. Here the three departments of government work in close, intimate contact, sharing some of the powers and functions of one another.

 

  1. Main Role of the Lower House in Ministry-formation: In the parliamentary government the lower house of the legislature, i.e., the popular chamber plays a vital role in the formation of the ministry. The leader of the party or alliance which wins the majority in this house is appointed the Prime Minister or Chancellor. The constitutional ruler appoints the other members of the ministry on his advice.

 

  1. Responsibility to the Legislature: In such a system the Cabinet or Ministry has to remain responsible to the legislature for all its activities and policies. In countries having bi-cameral legislatures, the Cabinet remains responsible to the lower house composed of the people’s representatives.

 

  1. Collective Responsibility: The ministerial responsibility to the legislature may again be of two kinds:

 

Individual responsibility, andCollective responsibility.

Individual responsibility means that the minister in charge of a department must be answerable for the activities of his department. But when the ministers remain jointly or collectively responsible to the legislature for the policies and activities of the government, it is called ‘collective responsibility’. Since no individual minister can unilaterally perform any business of government without the consent of the Cabinet, the entire Ministry or Cabinet has to remain accountable for the errors of the minister concerned.

 

  1. Intimate relationship between the Legislature and the Executive: In the parliamentary system an intimate relationship exists between the executive and the legislative departments. So they can easily control each other. The leaders of the majority party or alliance in the legislature become the members of the Cabinet or Ministry. Naturally, the ministers can easily extend their influence on the legislature. Consequently, the programs and policies of the Cabinet are backed by a majority inside the legislature.

 

  1. Leadership of the Prime Minister: The leadership of the Prime Minister is another major feature of the parliamentary system. The leader of the majority party in the legislature becomes the Prime Minister. Though, in theory, he is ‘primus inter pares’, i.e. ‘first among equals’, in reality, he possesses much greater power and status than the other ministers. As the undisputed leader of the majority party or alliance in the legislature he plays the most vital role in the determination and execution of government policies. Indeed, the success of parliamentary democracy depends, to a great extent, on the personality, efficiency and charisma of the Prime Minister.

 

  1. Existence of a Strong Opposition: The existence of one or more strong and well-organized opposition party or parties is the hall-mark of the parliamentary system. By criticizing the errors of the government, the opposition can compel it to adopt welfare measures and prevent it from becoming despotic. Judged from this angle, the opposition can be called the life-force of parliamentary democracy.

 

  1. Cabinet Dictatorship: In the parliamentary system of government the cabinet has to perform manifold functions.

 

It is the Cabinet which:

 

formulates well-considered policies of the Government after reviewing both the national and international issues,takes necessary, arrangements for passing laws to implement the policies formulated by it,determines the matters to be included in the agenda of the central legislature,controls and directs the administrative departments so that laws, Government orders, etc. are to be implemented properly,co-ordinates the activities of different departments of the Government,prepares the draft budget in consultation with the Prime Minister and takes necessary initiative to get it passed in the legislature,formulates economic policies and takes necessary steps for implementing the same,advice’s the constitutional head to take necessary action during emergency or unforeseen situation, etc.In this way the Cabinet acts as ‘the keystone of the political arch’ or has become the ‘steering wheel of the ship of the state’. In fact, in the parliamentary system of government as the cabinet members are the leaders of the majoity party or alliance in the legislature. Some critics think that the Parliament is controlled by the Cabinet under the leadership of the Prime Minister giving rise to some sort of “Cabinet dictatorship”.

 

Advantages :

 

The Parliamentary form of Government offers a lot of: advantages. The close cooperation between the executive and the legislative organs leades to smooth functioning of government and avoids unnecessary confrontation between them. These two organs work as mutually complementary to each other.

 

The responsibility of the government ensures an open administration. The executive, conscious of its responsibility to remain responsible for all its actions and to answer the question of the legislature relating to administration to their satisfaction always tries to remain alert, because this influences its electoral prospects. The more the mistake the less the chance of popular support in the election.

 

The system is flexible. Flexibility is an asset in any system as it provides room for adjustment. The parliamentary form of government is highly adaptive to changing situation. For example in times of grave emergency the leadership can be changed without any hassles, to tackle the situations as it happened during II World War in England. Mr. Chamberlain made way for Mr. Winston Churchil to handle the war. Even the election can be deferred till normalcy is restored. Such flexibility in the system does not exist in Presidential form of government which is highly rigid.

 

Under this system it is easier to locate responsibility for the lapses in administration. There is a vast body of civil servants who constitute the permanent executive. In fact they help the political masters to formulate policies of administration and their implementation. But it is the political leadership or the cabinet who takes the responsibility for everything in administration. Therefore it is said that the bureaucracy thrives under the cloak of ministerial responsibility.

 

A great merit of the system, as painted by Lord Bryce, if its swiftness in decision making. The executive can take any decision and quickly implement that without any hindrance. Since the party in power enjoys majority support in the legislature it can act freely without the fear of being let down.

 

Disadvantages:

 

However no system is completely foolproof. Advantages and disadvantages are part of any system irrespective of its soundness. Under this system the liberty of the people are at a stake as the executive and legislative organs of the government work in close collaboration. This greatly affects the principle of separation of powers. In view of the legislative support and the formidable power at its disposal the cabinet virtually becomes dictatorial. It becomes whimsical in exercising its power without caring for liberty of the people.

 

Politicization of administration is another demerit of the system. Political consideration in policy formulation and implementation outweigh popular interest. In other words people’s interest suffers at the cost of political considerations. The leadership of the party by virtue of powers it enjoys mobilizes the administration to strengthen the party prospects in the election.

 

The same can be said of the opposition parties who oppose the party in power for political considerations. They hardly show interest in the activities of the government and offer constructive criticism.

 

Prof. Dicey points out another serious lacuna in the system. According to him the executive under a parliamentary system fails to take quick decision at the time of any crisis or war. The members of the cabinet always are not unanimous on all problems. The Prime Minister discusses with his colleagues in the cabinet and ultimately prevails over them to take unanimous decision. This is different from the Presidential system where he takes the decision himself and implements that.

 

This system is unsuitable in countries with more than two parties. Usually in a multi party system the electorate fail to support a particular party in the election as a result of that there is hardly any party which gets majority votes. This leads to instability, chaos and confusion in selecting a party or a leader to form the government. As we observe the large number of political parties in India have contributed to political instability. Countries like Great Britain do not demonstrate such state of affairs as dual party system is the true basis of parliamentary democracy.

 

A criticism leveled against the Parliamentary system is that the government is run by the novice, ‘without any administrative training, skill or background. They are elected from social field and therefore depend heavily on the civil servants for formulation and implementation of policies. The bureaucrats under the system assume greater authority and consolidate their own position to use their political masters as mere tools.

Our constitution provides for parliamentary form of government. We have borrowed the constitutional features of several democratic countries. But our parliamentary model is predominantly based on the British system. The Head of Government in our system, the Prime Minister, can hold office only so long as he commands the confidence  of  the  Lok  Sabha.  Confidence  of  the  House  is  reflected  in existence/continuance of majority support – whether it be of a single party or of a coalition of parties. This feature can, and does, cause instability in governance. In Presidential democracies, the Head of Government, the President is directly elected by the people and cannot be removed from office except in circumstances of high crimes  and  misdemeanour  established  through  impeachment  process.  Hence, Presidential democracies provide stable governance. In our parliamentary system, we have had changes of government through mid term elections or political realignments. Changes in government undoubtedly bring about disruptions in implementation of policies, development programmes and schemes.

 

 

SOURCE OF FINANCE

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Sources of finance are the most explored area especially for the entrepreneurs about to start a new business. It is perhaps the toughest part of all the efforts. There are various sources of finance classified based on time period, ownership and control, and source of generation of finance.

 

The process of selecting right source of finance involves in-depth analysis of each and every source of finance. For analyzing and comparing the sources of finance, it is required to understand all characteristics of the financing sources. There are many characteristics on the basis of which sources of finance are classified.

On the basis of a time period, sources are classified into long term, medium term, and short term. Ownership and control classify sources of finance into owned capital and borrowed capital. Internal sources and external sources are the two sources of generation of capital. All the sources of capital have different characteristics to suit different types of requirements. Let’s understand them in a little depth.

 

ACCORDING TO TIME-PERIOD:

 

Sources of financing a business are classified based on the time period for which the money is required. Time period is commonly classified into following three:

  • Long Term Sources of Finance:

 

Long-term financing means capital requirements for a period of more than 5 years to 10, 15, 20 years or maybe more depending on other factors. Capital expenditures in fixed assets like plant and machinery, land and building etc of a business are funded using long-term sources of finance. Part of working capital which permanently stays with the business is also financed with long-term sources of finance. Long term financing sources can be in form of any of them:

 

  • Share Capital or Equity Shares
  • Preference Capital or Preference Shares
  • Retained Earnings or Internal Accruals
  • Debenture / Bonds
  • Term Loans from Financial Institutes, Government, and Commercial Banks
  • Venture Funding
  • Asset Securitization
  • International Financing by way of Euro Issue, Foreign Currency Loans, ADR, GDR etc.

 

  • Medium Term Sources of Finance:

 

Medium term financing means financing for a period of 3 to 5 years. Medium term financing is used generally for two reasons. One, when long-term capital is not available for the time being and second, when deferred revenue expenditures like advertisements are made which are to be written off over a period of 3 to 5 years. Medium term financing sources can in the form of one of them:

 

  • Preference Capital or Preference Shares
  • Debenture / Bonds
  • Medium Term Loans from
    • Financial Institutes
    • Government, and
    • Commercial Banks
  • Lease Finance
  • Hire Purchase Finance.

 

  • Short Term Sources of Finance: Short term financing means financing for a period of less than 1 year. Need for short term finance arises to finance the current assets of a business like an inventory of raw material and finished goods, debtors, minimum cash and bank balance etc. Short term financing is also named as working capital financing. Short term finances are available in the form of:

 

  • Trade Credit
  • Short Term Loans like Working Capital Loans from Commercial Banks
  • Fixed Deposits for a period of 1 year or less
  • Advances received from customers
  • Creditors
  • Payables
  • Factoring Services
  • Bill Discounting etc.

 

There are two main categories of sources from which the firm can get the required funds for their business. These are:

 

 (1) Internal sources; and

(2) External sources.

When the businessman invests his own money (called owner’s capital), and retains a part of the profits earned in the business it constitute the internal sources of finance. It is an integral part of every business organisation and it is cost effective. But, this source has its own limitations. Hence the business houses have to resort to the external sources of finance. The various external sources from where businessmen can get the finance include, friends and relatives, banks and other financial institutions, moneylenders, capital market, manufacturers and producers, customers, foreign financial institutions and agencies, etc. It is observed that the scope of raising funds also depends upon the nature and form of business organisation.

 

The following are the usual sources of finance. (a) Capital Market (b) Financial Institutions (c) Public Deposits (d) Commercial Banks (e) Leasing Companies (f) Investment Trusts (g) Retained Profits

DISCOUNT

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Discount

 

The discount is referred to the reduction in the price of some commodity or service. It may anywhere appear in the distribution channel in the form of modifications in marked price (printed on the item) or in retail price (set by retailer usually by pasting a sticker on the item) or in list price (quoted for the buyer). The discount is provided for the purpose of increasing sales, to clear out old stock, to encourage distributors, to reward potential customer etc. In short, the discount can serve as a way to attract customers for a particular item or service.

In math, discount is one of the easiest way to raise the customers of particular product. Discounts are a significant element of your online merchandising plan. You build discounts so that you can force sales on items or collection of products to your customers who convene particular conditions. In math, the discount problems can be solved by using discount formula.

The “discount rate” means the interest rate. Discount rate is based on the simple interest rate. To calculate simple interest rate, just find out the interest rate for one period (multiply by amount, interest rate, period) but calculate the discount rate, just multiply by the amount and an interest rate. This is called the define discount rate.

To calculate the discount rate, just multiply the amount by an interest rate. By using the Formula Discount rate DR = pr (p = principal amount, r = interest rate).

 

What is Discount Rate?

Discount rate is one of the simple ways to increase the customers of particular product. Discounts are a important element of your online merchandising strategy. You make discounts so that you can force sales on products or collection of products to your customers who meet certain particular conditions.

 

 

The formula used to calculate the discount is discount = marked price – selling price.

Here,

 

Selling price is what you actually pay for the item.

 

Marked price is the normal price of the item without a discount.

 

Discount is either a dollar rate or a percentage of the marked cost.

 

Discount Rate Definition

Discount Rate is the cost of the total amount generally less than its original value is called . In other words, a total bill will generally sell at a discount, and the discount rate is annualized percentage of this discount, that is percentage is adjusted to give an annual percentage.

 

Discount Rate Formula

Formula of the Discount Rate is:

 

Discount rate DR = pr

where,

  • p = principal amount
  • r = interest rate

 

 

 

Questions:

Level-I

1: Ricky purchase the dress. That dress rate was Rs1000 at 10% discount . Find discount rate? And then ricky how many dollars give to cashier?

2: Kalvin purchased land for 50000 dollars at 20% in 2000th year. Then 2004th year that land sales 3000 dollars. How many dollars he loss?

  1. The marked price of a ceiling fan is $ 1250 and the shopkeeper allows a discount of 6% on it. Find the selling price of the fan.
  2. A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain percent?
  3. A dealer purchased a washing machine for $ 7660. He allows a discount of 12% on its marked price and still gains 10%. Find the marked price of the machine.
  4. How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%?
  5. Find the single discount equivalent to two successive discounts of 20% and 10%.
  6. A merchant who marked his goods up by 50% subsequently offered a discount of 20% on the marked price. What is the percentage profit that the merchant make after offering the discount?

 

  1. Applied to a bill for Rs. 1,00,000 the difference between a discount of 40% and two successive discounts of 36% and 4% is:
  2. On a 20% discount sale, an article costs Rs. 596. What was the original price of the article?

Level-II:

  1. A discount of 15% on one article is the same as discount of 20% on a second article. The costs of the
  2. A discount of 2 ½% is given to the customer on marked price of an article. A man bought the article for Rs. 39. The marked price of article is:
  3. Printed price of an article is Rs. 900 but the retailer gets a discount of 40%. He sells the article for Rs. 900. Retailer’s gain percent is:
  4. The marked price of a watch was Rs. 720. A man bought the same watch for Rs. 550.80, after getting two successive discounts. If the first discount was 10%, what was the second discount rate?
  5. A shopkeeper marks his goods 20% above cost price, but allows 30% discount for cash. His net loss is:
  6. A retailer buys 40 pens at the marked price of 36 pens from a wholesaler. If he sells these pens giving a discount of 1%, what is the profit percent?
  7. A pizzeria has a coupon that reads, “Getoff a $9.00 cheese pizza.” What is the discount? What is the sale price of the cheese pizza?

18.In a video store, a DVD that sells for $15 is marked, “10% off.” What is the sale price of the DVD?

 

Answers:

Level-I:

 

Solution:1
Here,

Principal amount p = 1000 rs

Interest rate r = 10%

Discount rate DR = pr

DR = 1000*

= 100

The discount amount for the dress is 100.

Discount rate DR = 100.

Dress rate = principal amount – discount rate

= 1000 – 100

=900

Ricky gives 900 rs to cashier

 

 

Solution:2
Principal amount p = 50000 dollars

Interest rate r = 20%

Discount rate DR = pr

DR = 50000 x 2010020100 in 2000th year

= 10000

Discount rate DR = 1000 dollars in 2000th year.

The discount amount is 10000 dollars.

Discount rate DR = 50000*30/100 in 2004th year

Discount rate =15000 dollars.

The discount amount is 15000 dollars.

Loss Discount rate in 2004th year – Discount rate in 2000th year

=15000 dollars – 10000 dollars

=5000 dollars

Kalvin 5000 dollars losses in that land.
 

Solution:3

Marked price = $ 1250 and discount = 6%.

Discount = 6% of Marked Price

= (6% of $ 1250)

= $ {1250 × (6/100)}

= $ 75

Selling price = (Marked Price) – (discount) 

= $ (1250 – 75)

= $ 1175.

Hence, the selling price of the fan is $ 1175.

 

Solution:4

Let the cost price be $ 100.

Then, marked price = $ 140.

Discount = 25% of Marked Price 

= (25% of $ 140)

= $ {140 × (25/100)

= $ 35.

Selling price = (marked price) – (discount) 

= $ (140 – 35)

= $ 105.

Gain% = (105 – 100) % = 5%.

Hence, the trader gains 5%.

 

Solution:5

Cost price of the machine = $ 7660, Gain% = 10%.

Therefore, selling price = [{(100 + gain%)/100} × CP]

= $ [{(100 + 10)/100} × 7660]

= $ [(110/100) × 7660]

= $ 8426.

Let the marked price be $ x.

Then, the discount = 12% of $x

= $ {x × (12/100)}

= $ 3x/25

Therefore, SP = (Marked Price) – (discount)

= $ (x – 3x/25)

= $ 22x/25.

But, the SP = $ 8426.

Therefore, 22x/25 = 8426

⇒ x = (8426 × 25/22)

⇒ x = 9575.

Hence, the marked price of the washing machine is $ 9575

 

Solution:6

Let the cost price be $ 100.

Gain required = 20%.

Therefore, selling price = $ 120.

Let the marked price be $x.

Then, discount = 25% of $x

= $ (x × 25/100)

= $ x/4

Therefore, selling price = (Marked Price) – (discount)

= $ {x – (x/4)

= $ 3x/4

Therefore, 3x/4 = 120

⇔ x = {120 × (4/3)} = 160

Therefore, marked price = $ 160.

Hence, the marked price is 60% above cost price.

 

Solution:7

Let the marked price of an article be $ 100.

Then, first discount on it = $ 20.

Price after first discount = $ (100 – 20) = $ 80.

Second discount on it = 10% of $ 80

= $ {80 × (10/100)} = $ 8.

Price after second discount = $ (80 – 8) = $ 72.
Net selling price = $ 72.

Single discount equivalent to given successive discounts = (100 – 72)% = 28%

 

Solution:8 The easiest way to solve these kinds of problems is to assume a value for the merchant’s cost price.
To make calculations easy, it is best to assume the cost price to be $100.

The merchant marks his goods up by 50%.
Therefore, his marked price (quoted price) = cost price + mark up.
Marked price = $100 + 50% of $100 = 100 + 50 = $150.

The merchant offers a discount of 20% on his marked price.
Discount offered = 20% of 150 = $30.

Therefore, he finally sold his goods for $150 – $30 = $ 120.
We assumed his cost to be $100 and he sold it finally for $120.

Therefore, his profit = $20 on his cost of $ 100.
Hence, his % profit = profit/cost price * 100 = 20/100*100  = 20%.

 

Solution:9 40% of Rs. 1,00,000 = Rs. 40,000
36% of 1,00,000 = 36000
4% of 36,000 = Rs. 2,560.
Therefore, two successive discounts on Rs. 1,00,000 = 36,000 + 2560 = Rs. 38,560.
Difference between a discount of 40% and two successive discounts of 36% and 4%
= 40,000 – 38,560
= Rs. 1,440

Solution:10 If the selling price of the article is S, then
S – 20% of S = 596
S – S/5 = 596
4S/5 = 596
⇒ S = 596 x 5/4
⇒ S = 745

Level-II

Solution:11Let the prices of two articles be X and Y
From the question 15X/100 = 20Y/100
X/Y = 20/15
Thus the ratio of prices of two articles is 4 : 3
Any two amounts in the ratio 4 : 3 will satisfy the condition.
In the above instance, Rs. 80 and Rs. 60 is the answer.

Solution:12 Formula for Marked Price = 100 x SP/(100 – d%) = 100 x 39/(100 – 2.5%)
= 3900 / 97.5
= Rs. 40.
Marked Price of Article is Rs. 40.

Solution:13 Retailer gets a discount of 40% means he buys it at 60% of the price
60% x 900 = Rs. 540
Profit on selling it at Rs. 900 = 900 – 540 = Rs. 360.
Profit % = (Profit / C.P) x 100 = (360 / 540) x 100 = 662/3
Retailer’s Gain percent is 662/3

Solution:1410% discount on 720 = Rs. 72
Cost after 1st discount = 720 – 72 = Rs. 648.
Cost after 2nd discount = Rs. 550.80
Therefore 2nd discount = 648 – 550.80 = Rs. 97.20
Discount % = (97.2 x 100)/648 = 15%
Second discount rate = 15%.

Solution:15 Let the cost price be Rs. 100.
M.P. (which is 20% above C.P.) = Rs. 120.
30% discount on Rs. 120 = Rs. 36.
Selling Price = Rs. 120 – 36 = Rs. 84
Cost Price = Rs 100 and Selling Price = Rs 84 {since CP > SP, it is a loss}
Loss% = (16/100) x 100 = 16%.
His net loss percent is 16%.

Solution:16 Assuming the M.P. of each pen to be Rs. 10, the M.P. of 36 pens = Rs. 360
Cost price of 40 pens = Rs. 360 (from the question)
Cost price of each pen = 360/40 = Rs. 9
Selling Price of each pen at a discount of 1% on a marked price of Rs. 10 = 99% x 10 = Rs. 9.90
Profit = 9.90 – 9.00 = Rs. 0.90
Profit % = (0.90/9.00) x 100 = 10%
Profit % = 10%.

Solution:17 The discount is $3.00 and the sale price is $6.00

Solution:18 The rate is 10%. Thus, the customer is paying 90% for the DVD

The sale price is: 0.90 x $15.00 = $13.50

The sale price is $13.50.

BUDGETING

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Budgeting

Budgeting is the process of estimating the availability of resources and then allocating them to various activities of an organization according to a pre-determined priority. In most cases, approval of a budget also means the approval to various spending units to utilize the allocated resources. Budgeting plays a criucial role in the socio-economic development of the nation.

Budget is the annual statement of the outlays and tax revenues of the government of India together with the laws and regulations that approve and support those outlays and tax revenues . The budget has two purposes in general :
1. To finance the activities of the union government
2. To achieve macroeconomic objectives.

The Budget contains the financial statements of the government embodying the estimated receipts and expenditure for one financial year, ie.  it is a proposal of how much money is to be spent on what and how much of it will
be contributed by whom or raised from where during the coming year.

Different types of Budgeting

Economists throughout the globe have classified the budgets into different types based on the process and purpose of the budgets, which are as follows:-

1- The Line Item Budget

line-item budgeting was introduced in some countries in the late 19th centuary. Indeed line item budgeting which is the most common form of budgeting in a large number of countries and suffers from several drawbacks was a major reform initiative then. The line item budget is defined as “the budget in which the individual financial statement items are grouped by cost centers or departments .It shows the comparison between the financial data for the past  accounting or budgeting periods and estimated figures for the current or a future period”In a line-item system, expenditures for the budgeted period are listed according to objects of expenditure, or “line-items.” These line items include detailed ceilings on the amount a unit would spend on salaries, travelling allowances, office expenses, etc. The focus is on ensuring that the agencies
or units do not exceed the ceilings prescribed. A central authority or the Ministry of Finance keeps a watch on the spending of various units to ensure that the ceilings are not violated. The line item budget approach is easy to understand and implement. It also facilitates centralized control and fixing of authority and responsibility of the spending units. Its major disadvantage is that it does not provide enough information to the top levels about the activities and achievements of individual units.

2 – Performance Budgeting

a performance budget reflects the goal/objectives of the organization and spells out performance targets. These targets are sought to be achieved through a strategy. Unit costs are associated with the strategy and allocations are accordingly made for achievement of the objectives. A Performance Budget gives an indication of how the funds spent are expected to give outputs and ultimately the outcomes. However, performance budgeting has a limitation – it is not easy to arrive at standard unit costs especially in social programmes which require a multi-pronged approach.

3- Zero-based Budgeting

The concept of zero-based budgeting was introduced in the 1970s. As the name suggests, every budgeting cycle starts from scratch. Unlike the earlier systems where only incremental changes were made in the allocation, under zero-based budgeting every activity is evaluated each time a budget is made and only if it is established that the activity is necessary, are funds allocated to it. The basic purpose of Zero-based Budgeting is phasing out of programmes/ activities which do not have relevance anymore. However, because of the efforts involved in preparing a zero-based budget and institutional resistance related to personnel issues, no government ever implemented a full zero-based budget, but in modified forms the basic principles of ZBB are often used.

4- Programme Budgeting and Performance Budgeting

Programme budgeting in the shape of planning, programming and budgeting system (PPBS) was introduced in the US Federal Government in the mid-1960s. Its core themes had much in common with earlier strands of performance budgeting.
Programme budgeting aimed at a system in which expenditure would be planned and controlled by the
objective. The basic building block of the system was classification of expenditure into programmes, which meant objective-oriented classification so that programmes with common objectives are considered together.
It aimed at an integrated expenditure management system, in which systematic policy and expenditure planning would be developed and closely integrated with the budget. Thus, it was too ambitious in scope. Neither was adequate preparation time given nor was a stage-by-stage approach adopted. Therefore, this attempt to introduce PPBS in the federal government in USA did not succeed, although the concept of performance budgeting and programme budgeting endured.

 

 

Budgetary Control

Budgetary control refers to how well managers utilize budgets to monitor and control costs and operations in a given accounting period. In other words, budgetary control is a process for managers to set financial and performance goals with budgets, compare the actual results, and adjust performance, as it is needed.

Budgetary control involves the following steps :

(a) The objects are set by preparing budgets.

(b) The business is divided into various responsibility centres for preparing various budgets.

(c) The actual figures are recorded.

(d) The budgeted and actual figures are compared for studying the performance of different cost centres.

(e) If actual performance is less than the budgeted norms, a remedial action is taken immediately.

The main objectives of budgetary control are the follows:

  1. To ensure planning for future by setting up various budgets, the requirements and expected performance of the enterprise are anticipated.
  2. To operate various cost centres and departments with efficiency and economy.
  3. Elimination of wastes and increase in profitability.
  4. To anticipate capital expenditure for future.
  5. To centralise the control system.
  6. Correction of deviations from the established standards.
  7. Fixation of responsibility of various individuals in the organization.

 

Responsibility Accounting

Responsibility accounting is an underlying concept of accounting performance measurement systems. The basic idea is that large diversified organizations are difficult, if not impossible to manage as a single segment, thus they must be decentralized or separated into manageable parts.

These decentralized parts are divided as : 1) revenue centers, 2) cost centers, 3) profit centers and 4) investment centers.

  1. revenue center (a segment that mainly generates revenue with relatively little costs),
  2. costs for a cost center (a segment that generates costs, but no revenue),
  3. a measure of profitability for a profit center (a segment that generates both revenue and costs) and
  4. return on investment (ROI) for an investment center (a segment such as a division of a company where the manager controls the acquisition and utilization of assets, as well as revenue and costs).

 

Advantages:-

  1. It provides a way to manage an organization that would otherwise be unmanageable.
  2. Assigning responsibility to lower level managers allows higher level managers to pursue other activities such as long term planning and policy making.
  3. It also provides a way to motivate lower level managers and workers.
  4. Managers and workers in an individualistic system tend to be motivated by measurements that emphasize their individual performances.

In India the budget is prepared from top to bottom approach and responsible accounting would not only improve the efficiency of Indian budgetary system but also will help in performance analysis.

Social Accounting

Social accounting is concerned with the statistical classification of the activities of human beings and human institutions in ways which help us to understand the operation of the economy as a whole.

Social accounting is the process of communicating the social and environmental effects of organizations’ economic actions to particular interest groups within society and to society at large

The components of social accounting are production, consumption, capital accumulation, government transactions and transactions with the rest of the world.

The uses of social accounting are as follows:

(1) In Classifying Transactions

(2) In Understanding Economic Structure

(3) In Understanding Different Sectors and Flows

(4) In Clarifying Relations between Concepts

(7) In Explaining Movements in GNP

(8) Provide a Picture of the Working of Economy

(9) In Explaining Interdependence of Different Sectors of the Economy

(10) In Estimating Effects of Government Policies

(11) Helpful in Big Business Organisations

(12) Useful for International Purposes

(13) Basis of Economic Models

 

Budgetary Deficit

Budgetary Deficit is the difference between all receipts and expenditure of the government, both revenue and capital. This difference is met by the net addition of the treasury bills issued by the RBI and drawing down of cash balances kept with the RBI. The budgetary deficit was called deficit financing by the government of India. This deficit adds to money supply in the economy and, therefore, it can be a major cause of inflationary rise in prices.

Budgetary Deficit of central government of India was Rs. 2,576 crores in 1980-81, it went up to Rs. 11,347 crores in 1990-91 to Rs. 13,184 crores in 1996-97.

The concept of budgetary deficit has lost its significance after the presentation of the 1997-98 Budget. In this budget, the practice of ad hoc treasury bills as source of finance for government was discontinued. Ad hoc treasury bills are issued by the government and held only by the RBI. They carry a low rate of interest and fund monetized deficit. These bills were replaced by ways and means advance. Budgetary deficit has not figured in union budgets since 1997-98. Since 1997-98, instead of budgetary deficit, Gross Fiscal Deficit (GFD) became the key indicator.

 

Fiscal Deficit

  • The difference between total revenue and total expenditure of the government is termed as fiscal deficit. It is an indication of the total borrowings needed by the government and thus amounts to all the borrowings of the government . While calculating the total revenue, borrowings are not included.
  • The gross fiscal deficit (GFD) is the excess of total expenditure including loans net of recovery over revenue receipts (including external grants) and non-debt capital receipts. The net fiscal deficit is the gross fiscal deficit less net lending of the Central government.
  • Generally fiscal deficit takes place either due to revenue deficit or a major hike in capital expenditure. Capital expenditure is incurred to create long-term assets such as factories, buildings and other development.
  • A deficit is usually financed through borrowing from either the central bank of the country or raising money from capital markets by issuing different instruments like treasury bills and bonds.

 

Revenue Deficit

  • Revenue deficit is concerned with the revenue expenditures and revenue receipts of the government. It refers to excess of revenue expenditure over revenue receipts during the given fiscal year.
  • Revenue Deficit = Revenue Expenditure – Revenue Receipts
  • Revenue deficit signifies that government’s own revenue is insufficient to meet the expenditures on normal functioning of government departments and provisions for various services.
  • In India social expenditure like MNREGA is a revenue expenditure though a part of Plan expenditure.
  • Its targeted to be 2.9% of GPD in the year 2014-15, though the fiscal revenue and budget management act specifies it to be zero by 2008-09

functional classification of urban settlements Problems of human settlement in India

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The definition of function varies across the disciplines. In political science it refers to duties, in mathematics it means the relationship between two variables and in geography it is synonymous to occupation.

Geographers have classified towns on the basis of their site, situation, size, rank, location and relative elevation. Functional classification of towns attempts to categorize towns and cities according to their economic functions, thereby identifying their roles within urban systems. Most classifications use employment and occupational data. In the functional classification approach, towns are classified on the basis of their dominant function. The functional classification of towns has been illus­trated in the following paras:

1.)Administrative town

The main function of administrative cities and towns is to administer the country/state or a specific territory.It includes not only the capital cities of countries, but all the centres of provinces, states, districts and other administrative divisions of the country.

2.Defensive Towns:

During the medieval period, most of the towns and cities used to be developed on the defensive sites.Forts and garrisons used to be constructed at strategic places. The defensive towns have barracks, cantonments, and training facilities for the armed forces, airfields, and harbours for warships.Visakhapatnam, MHOW and Khadakwasla (India);

In many garrison and defensive towns, there is a clear division of land use between the civil and military authorities, so that the military installa­tions are often at a little distance from the town or are grouped together in one part of the town. This is necessary to maintain security, though often many town people are employed by the military.

3.Cultural Centres:

There are numerous towns and cities in the world, almost in each of the countries, which perform cultural functions.The cities of Oxford and Cambridge in England are the most suitable examples of educational towns. In these towns, one may find colleges, libraries, hostels, churches, playgrounds, parks and shopping centres. The environmental pollution in these towns is almost insignificant.

4.) Collection Centres:

The mining towns, fishing ports and lumbering centres fall under the category of collection centres/towns. There are numerous metallic, non-metallics, precious stones and energy resources which are obtained from mines.The towns which serve these mines may be small settlements serving a particular mine such as Zawar near Udaipur (Rajasthan), Bjiladela (Madhya Pradesh) and Digboi (Assam).They may be large in size such as Raniganj, Hazaribagh (Bihar), Ipoh in the tin rich Kinta valley of Malaysia, or Kuwait and Abadan in the oil producing regions of Kuwait and Tehran, respectively.Such towns may have some industries related to the mineral mines, such as smelters and refineries. The shops in such towns sell mining equipments and special clothes needed for miners.

5.) Production Centres:

Urban places, town and cities in which some kind of manufacturing industry is the major function is known as a production centre. The size and appearance of the town are affected by the type of industry located there.

  • For example, Jamshedpur, Rourkela, Bhilai, Durgapur, Dhanbad and Bhadravati in India, Pittsburgh in USA, Magnitogorsk in Russia and Birmingham in UK are dominated by large steel plants. Such iron and steel producing towns are generally located near the coal fields.
  • For the manufacturing towns, as collecting centres, transportation is very important for the transport of raw materials and the finished goods. These days such towns are generally set up on lines of communication.

In manufacturing towns, there is a segregation of houses and estab­lishments; the officer’s quarters may be grouped at one place and that of the labourers at the other.

6.) Towns of Diversified Functions:

As stated at the outset, towns are classified according to their major functions. So, all those towns (such as Mumbai, Kolkata, Chennai, etc.) can be put into a definite category in which a large number of activities are conducted. Such towns are referred as diversified in functions.

Over space and time, the functions of towns change. For example, defensive sites often become restrictive when the town expands.Thus, many towns have restricted centres which were once confined within the town walls and more extensive suburbs which grew up outside the walls or after the walls were demolished.

Shahjahanabad (old Delhi), Padova (Italy), Lahore and Rawalpindi (Pakistan), Baghdad (Iraq) and Baku (Azerbaijan) are some of the examples of such towns.

7.)Residential Towns:

In some towns, the chief function is simply to house a concentration of population. In such areas, most of the land is devoted to houses, parks and hospitals. These towns are very- well-connected with the major cities, which enables the commuters to get to work each day.

  1.  Resorts:

The urban places which cater to the recreation needs of people are known as resorts or recreation towns.These urban places may be based on health-giving water (hot springs), seaside recreation, mountain climbing, cultural attractions, historical monuments, sports facilities, national parks and attractive scenery.Resorts and recreational towns have many hotels to accommodate visitors, and also provide sporting facilities such as golf courses, swimming pools, trekking and skiing. Moreover, they have numerous entertainment facilities, such as theatres, cinemas, and night clubs and children parks.

  1. Transfer and Distribution Centres:

The main functions performed at transfer centres are the trade, commerce and services. Towns which are concerned with the transfer and distribution of goods, however, have trade as their major function.

They include several types of towns. For example, market towns, sea ports and financial towns.Market towns are characterized by markets, a wide range of shops, stores, warehouses, godowns, cold storages and wholesale .markets.Market towns also have banks, insurance companies and other financial organizations. Kanpur, Ahmedabad, Vadodara, Indore, Bhopal, Patna, Lucknow, Ludhiana and Hapur in India, Norwich in England, Alexandria in Egypt, and Kumasi in Ghana are some of the examples of such towns.

 

Problem of Human settlement:

Some of the major problems of urbanisation in India are

  1. Urban Sprawl

Urban sprawl or real expansion of the cities, both in population and geographical area, of rapidly growing cities is the root cause of urban problems. In most cities the economic base is incapable of dealing with the problems created by their excessive size

  1. Overcrowding

Overcrowding is a situation in which too many people live in too little space. Overcrowding is a logical consequence of over-population in urban areas. It is naturally expected that cities having a large size of population squeezed in a small space must suffer from overcrowding. This is well exhibited by almost all the big cities of India.

 

3.Slums and Squatter Settlements:

The natural sequel of unchecked, unplanned and haphazard growth of urban areas is the growth and spread of slums and squatter settlements which present a striking feature in the ecological structure of Indian cities, especially of metropolitan centres.

 

4.)Overcrowding

Overcrowding leads to a chronic problem of shortage of houses in urban areas. This problem is specifically more acute in those urban areas where there is large influx of unemployed or underemployed immigrants who have no place to live in when they enter cities/towns from the surrounding areas.

5.)Seweage problem

Urban areas in India are almost invariably plagued with insufficient and inefficient sewage facilities. Not a single city in India is fully sewered. Resource crunch faced by the municipalities and unauthorised growth of the cities are two major causes of this pathetic state of affairs.

Origin and evolution of earth

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Beginning of the Universe started about 13.6 billion years ago,when the Big Bang created the universe from a point source.
During this process, light elements, like H, He, Li, B, and Be formed. From this point in time, the universe began to expand and has been expanding ever since.
Concentrations of gas and dust within the universe eventually became galaxies consisting of millions of stars.
Within the larger stars, nuclear fusion processes eventually created heavier elements, like C, Si, Ca, Mg, K, and Fe.
Stars eventually collapse and explode during an event called a supernova. During a supernova, heavier elements, from Fe to U, are formed. (See figure 1.9 in your text).
Throughout galaxies clusters of gas attracted by gravity start to rotate and accrete to form stars and solar systems. For our solar system this occurred about 4.6 billion years ago.
The ball at the center grows dense and hot, eventually nuclear fusion reactions start and a star is born (in our case, the sun).
Rings of gas and dust orbiting around the sun eventually condenses into small particles. These particles are attracted to one another and larger bodies called planetismals begin to form.
Planetesimals accumulate into a larger mass. An irregularly-shaped proto-Earth develops.
The interior heats and becomes soft. Gravity shapes the Earth into a sphere. The interior differentiates into a nickel-iron core, and a stony (silicate) mantle.
Soon, a small planetoid collides with Earth. Debris forms a ring around the Earth.The debris coalesces and forms the Moon.
The atmosphere develops from volcanic gases. When the Earth becomes cool enough, moisture condenses and accumulates, and the oceans are born.

DESERT ECOSYSTEM

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Deserts are formed in regions with less than 25 cm of annual rainfall, .or sometimes in hot regions where there is more rainfall, but unevenly distributed in the annual cycle.

Lack’ of rain in the mid latitude is often due to stable high pressure zones; deserts in temperate regions often lie in “rain shadows”, that is where high mountains block off moisture from the seas.

The climate:of these biomes is modified by altitUde and latitude. At greater distance from the equator the deSerts are cold and hot near equator and tropics.

As the large volume of water passes through the irrigation system, salts may be left behind that will gradually accumulate over the years until they become limiting, unless means of avoiding this difficulty are devised

Adaptations

(i)  These plants conserve water by following methods:

They are mostly shrubs. Leaves are absent or reduced in size.

Leaves and stem are succulent and water storing.

In some plants even the stem contains chlorophyll for photosynthesis.

Root system is well developed and spread over large area.

The annuals wherever present germinate, bloom and reproduce only during the short rainy season, and not in summer and winter.

(ii) The animals are physiologically and behaviorally adapted to desert conditions.

They are fast runners.

They are nocturnal in habit to avoid the sun’s heat during day time.

They conserve water by excreting concentrated urine.

Animals and birds usually have long legs to keep the body away from the hot ground.

Lizards are mostly insectivorous and can live without drinking water for several days.

Herbivorous animals get sufficient water from the seeds which they eat.

Mammals as a group are poorly adapted to  deserts

Indian Desert — Thar desert (hot)

The climate of this region is characterised by excessive drought, the rainfall being scanty and , irregular.

The winter rains of northern India rarely penetrate into the region.

The proper desert plants may be divided into two main groups.

  1. i) depending directly upon on rain and
  2. ii) those depending on the presence of subterranean water.

The first group consists of two types:

the ‘ephemera’s’ and the rain perennials’.

The ephemera’s are delicate annuals, apparently free from any xerophilous adaptations, having slender stems and root-systems and often large Flowers.

They appear almost immediately after rain, develop flowers and fruits in an incredibly short   time, and die as soon as the surface layer of the soil dries up.

The rain perennials are visible above the ground only during the rainy season, but have a perennial underground stem.

The second group – depending on the presence of subterranean water

By far the largest number of indigenous plants are capable of absorbing water from deep below the surface of the ground by means of a well-developed root system, the main part of which generally consists of a slender, woody tap root of extraordinary length.

Generally, various other xerophilous adaptations are resorted to such as reduced leaves, thick hairy growth, succulence, coatings of wax, thick cuticle, protected stomata, etc., all having for  their object of reduction of transpiration.

 

Fauna

It is home to some of India’s most magnificent grasslands and sanctuary for a charismatic bird, the Great Indian Bustard. Among the mammal fauna, the blackbuck, wild ass, chinkara, caracal, Sandgrouse and desert fox inhabit the open plains, grasslands, and saline depressions.

The nesting ground of Flamingoes and the only known population of Asiatic wild Ass lies in the remote part of Great Rarm, Gujarat.

It is the migration flyway used by cranes and flamingos.

Some endemic flora species of Thar Desert includes Calligonum Polygonoides, Prosopis cineraria, Tecomella undulate, Cenchrus biflorus and Sueda fruticosa , etc

 

Cold Desert/ Temperate Desert

Cold desert of India include areas of ladak, leh and kargil of kashmir and spiti valley of Himachal  Pradesh and some parts of northern Uttaranchal and Sikkim. Lies in rain shadow of Himalaya Oak, pine, deodar, birch and rhododendron are the important trees and bushes found there. Major  animal include yaks, dwarf cows, and goats.

Severe arid conditions – Dry Atmosphere

Mean annual rainfall less than 400mm

Soil type – sandy to sandy loam , Soil pH – neutral to slight alkaline.

Soil nutrient – Poor organic matter content ,low water retention capacity

Bio-diversity

Cold desert is the home of highly adaptive, rare endangered fauna, such as

Asiatic Ibex, Tibetan Argali, Ladakh Uriyal, Bharal, Tibetan Antelope (chiru),

Tibetan Gazelle, Wild Yak, Snow Leopard, Brown Bear, Tibetan Wolf, Wild

Dog and Tibetan Wild Ass (‘Kiang’ a close relative of the Indian wild ass) ,

Woolly hare, Black Necked  Crane, etc.

India as a signatory to United Nations Convention to Combat Desertification

(UNCCD) has submitted four National Reports to UNCCD

in the years 2000, 2002, 2006 and 2010

Some of the major programmes currently implemented that address issues related to land degradation and desertification is:-

  1. Integrated Watershed Management Programme (IWMP),
  2. National Afforestation Programme (NAP),
  3. National Mission for Green India (GIM),
  4. The Mahatma Gandhi National Rural Employment Guarantee Scheme
  5. (MGNREGS),
  6. Soil Conservation in the Catchment of River Valley Project and Flood Prone River,
  7. National Watershed Development Project for Rainfed Areas (NWDPRA),
  8. Desert Development Programme (DDP)
  9. Fodder and Feed Development Scheme-component of Grassland Development including
  10. Grass Reserves, Command Area Development and Water Management (CADWM)  programme etc

 

 

SQUARE ROOT & CUBE ROOTS

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Square Root & Cube Root

 

Step 1: First of all group the number in pairs of 2 starting from the right.

 

Step 2: To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from left and put the square root of the square.

 

Step 3: To get the unit’s place digit of the square root

 

Remember the following

If number ends in Unit’s place digit of the square root
1 1 or 9(10-1)
4 2 or 8(10-2)
9 3 or 7(10-3)
6 4or 6(10-4)
5 5
0 0

 

Lets see the logic behind this for a better understanding

We know,

12=1

22=4

32=9

42=16

52=25

62=36

72=49

82=64

92=81

102=100

 

Now, observe the unit’s place digit of all the squares.

Do you find anything common?

 

We notice that,

Unit’s place digit of both 12 and 92 is 1.

Unit’s place digit of both 22 and 82 is 4

Unit’s place digit of both 32 and 72 is 9

Unit’s place digit of both 42 and 62 is 6.


Step 4: Multiply the ten’s place digit (found in step 1) with its consecutive number and compare the result obtained with the first pair of the original number from left.

 

Remember,

If first pair of the original number > Result obtained on multiplication then  select the greater number  out of the two numbers as the unit’s place digit of the square root.

 

If firstpair of the original number < the result obtained on multiplication,then select the lesser number out of the two numbers as the unit’s place digit of the square root.

 

 

Let us consider an example to get a better understanding of the method

 

 

Example 1: √784=?

Step 1: We start by grouping the numbers in pairs of two from right as follows

7 84

 

Step 2: To get the ten’s place digit,

We find that nearest square to first group (7) is 4 and √4=2

Therefore ten’s place digit=2

 

Step 3: To get the unit’s place digit,

We notice that the number ends with 4, So the unit’s place digit of the square root should be either 2 or 8(Refer table).

 

Step 4: Multiplying the ten’s place digit of the square root that we arrived at in step 1(2) and its consecutive number(3) we get,

2×3=6
ten’s place digit of original number > Multiplication result
7>6
So we need to select the greater number (8) as the unit’s place digit of the square root.
Unit’s place digit =8

Ans:√784=28

 

 

 

Cube roots of perfect cubes

It may take two-three minutes to find out cube root of a perfect cube by using conventional method. However we can find out cube roots of perfect cubes very fast, say in one-two seconds using Vedic Mathematics.

We need to remember some interesting properties of numbers to do these quick mental calculations which are given below.

 

Points to remember  for speedy  calculation of cube roots

  1. To calculate cube root of any perfect cube quickly, we need to remember the cubes of 1 to 10 which is given below.
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216
73 = 343
83 = 512
93 = 729
103 = 1000
  1. From the above cubes of 1 to 10, we need to remember an interesting property.
13 = 1 => If last digit of the perfect cube = 1, last digit of the cube root = 1
23 = 8 => If last digit of the perfect cube = 8, last digit of the cube root = 2
33 = 27 => If last digit of the perfect cube = 7, last digit of the cube root = 3
43 = 64 => If last digit of the perfect cube = 4, last digit of the cube root = 4
53 = 125 => If last digit of the perfect cube =5, last digit of the cube root = 5
63 = 216 => If last digit of the perfect cube = 6, last digit of the cube root = 6
73 = 343 => If last digit of the perfect cube = 3, last digit of the cube root = 7
83 = 512 => If last digit of the perfect cube = 2, last digit of the cube root = 8
93 = 729 => If last digit of the perfect cube = 9, last digit of the cube root = 9
103 = 1000 => If last digit of the perfect cube = 0, last digit of the cube root = 0

 

It’s very easy to remember the relations given above because

1 -> 1 (Same numbers)
8 -> 2 (10’s complement of 8 is 2 and 8+2 = 10)
7 -> 3 (10’s complement of 7 is 3 and 7+3 = 10)
4 -> 4 (Same numbers)
5 -> 5 (Same numbers)
6 -> 6 (Same numbers)
3 -> 7 (10’s complement of 3 is 7 and 3+7 = 10)
2 -> 8 (10’s complement of 2 is 8 and 2+8 = 10)
9 -> 9 (Same numbers)
0 -> 0 (Same numbers)

 

Also see
8 ->  2 and 2 ->  8
7 -> 3 and 3-> 7

 

 

 

 

 

Questions

Level-I

1. The cube root of .000216 is:
A. .6
B. .06
C. 77
D. 87

 

 

2.
What should come in place of both x in the equation x = 162 .
128 x
A. 12
B. 14
C. 144
D. 196

 

3. The least perfect square, which is divisible by each of 21, 36 and 66 is:
A. 213444
B. 214344
C. 214434
D. 231444

 

4. 1.5625 = ?
A. 1.05
B. 1.25
C. 1.45
D. 1.55

 

5. If 35 + 125 = 17.88, then what will be the value of 80 + 65 ?
A. 13.41
B. 20.46
C. 21.66
D. 22.35
 

 

6.

  

 

If a = 0.1039, then the value of 4a2 – 4a + 1 + 3a is:
A. 0.1039
B. 0.2078
C. 1.1039
D. 2.1039

 

7.
If x = 3 + 1 and y = 3 – 1 , then the value of (x2 + y2) is:
3 – 1 3 + 1
A. 10
B. 13
C. 14
D. 15

 

8. A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:
A. 57
B. 67
C. 77
D. 87

 

9. The square root of (7 + 35) (7 – 35) is
A. 5
B. 2
C. 4
D. 35

 

 

 

 

10.
If 5 = 2.236, then the value of 5 – 10 + 125 is equal to:
2 5
A. 5.59
B. 7.826
C. 8.944
D. 10.062

 

 

 

Level-II

 
11.
625 x 14 x 11 is equal to:
11 25 196
A. 5
B. 6
C. 8
D. 11

 

12. 0.0169 x ? = 1.3
A. 10
B. 100
C. 1000
D. None of these

 

13.
3 – 1 2 simplifies to:
3
A.
3
4
B.
4
3
C.
4
3
D. None of these

 

14. How many two-digit numbers satisfy this property.: The last digit (unit’s digit) of the square of the two-digit number is 8 ?
A. 1
B. 2
C. 3
D. None of these

 

15. The square root of 64009 is:
A. 253
B. 347
C. 363
D. 803

 

 

16. √29929 = ?
A. 173
B. 163
C. 196
D. 186

 

 

 

 

 

 

17. √106.09 = ?
A. 10.6
B. 10.5
C. 10.3
D. 10.2
 
 

 

 

18.  ?/√196 = 5
A. 76
B. 72
C. 70
D. 75
 
 

 

Answers

Level-I

 

Answer:1 Option B

 

Explanation:

(.000216)1/3 = 216 1/3
106

 

   = 6 x 6 x 6 1/3
102 x 102 x 102

 

   = 6
102

 

   = 6
100

= 0.06

 

Answer:2 Option A

 

Explanation:

Let x = 162
128 x

Then x2 = 128 x 162

= 64 x 2 x 18 x 9

= 82 x 62 x 32

= 8 x 6 x 3

= 144.

x = 144 = 12.

 

Answer:3 Option A

 

Explanation:

L.C.M. of 21, 36, 66 = 2772.

Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square, it must be multiplied by 7 x 11.

So, required number = 22 x 32 x 72 x 112 = 213444

 

Answer:4 Option B

 

Explanation:

1|1.5625( 1.25

|1

|——-

22| 56

| 44

|——-

245| 1225

| 1225

|——-

|    X

|——-

1.5625 = 1.25.

 

 

Answer:5 Option D

 

Explanation:

35 + 125 = 17.88

35 + 25 x 5 = 17.88

35 + 55 = 17.88

85 = 17.88

5 = 2.235

80 + 65 = 16 x 5 + 65

= 45 + 65

= 105 = (10 x 2.235) = 22.35

 

 

 

Answer:6 Option C

 

Explanation:

4a2 – 4a + 1 + 3a = (1)2 + (2a)2 – 2 x 1 x 2a + 3a

= (1 – 2a)2 + 3a

= (1 – 2a) + 3a

= (1 + a)

= (1 + 0.1039)

= 1.1039

 

Answer:7 Option C

 

Explanation:

x = (3 + 1) x (3 + 1) = (3 + 1)2 = 3 + 1 + 23 = 2 + 3.
(3 – 1) (3 + 1) (3 – 1) 2

 

y = (3 – 1) x (3 – 1) = (3 – 1)2 = 3 + 1 – 23 = 2 – 3.
(3 + 1) (3 – 1) (3 – 1) 2

x2 + y2 = (2 + 3)2 + (2 – 3)2

= 2(4 + 3)

= 14

 

Answer:8 Option C

 

Explanation:

Money collected = (59.29 x 100) paise = 5929 paise.

Number of members = 5929 = 77

 

 

Answer:9 Option B

 

Explanation:

(7 + 35)(7 – 35) = (7)2 – (35)2  = 49 – 45  = 4  = 2

 

 

Answer:10 Option B

 

Explanation:

5 – 10 + 125 = (5)2 – 20 + 25 x 55
2 5 25

 

= 5 – 20 + 50
25

 

= 35 x 5
25 5

 

= 355
10

 

= 7 x 2.236
2

 

= 7 x 1.118

 

= 7.826

 

 

Level-II

Answer:11 Option A

 

Explanation:

Given Expression = 25 x 14 x 11 = 5.
11 5 14

 

 

 

Answer:12 Option B

 

Explanation:

Let 0.0169 x x = 1.3.

Then, 0.0169x = (1.3)2 = 1.69

 x = 1.69 = 100
0.0169

 

 

 

Answer:13 Option C

 

Explanation:

3 – 1 2 = (3)2 + 1 2 – 2 x 3 x 1
3 3 3

 

= 3 + 1 – 2
3

 

= 1 + 1
3

 

= 4
3

 

 

 

Answer:14 Option D

 

Explanation:

A number ending in 8 can never be a perfect square.

 

 

Answer:15 Option A

 

Explanation:

2 |64009( 253      |4      |———-45  |240      |225      |———-503| 1509      |  1509      |———-      |     X      |———-

64009 = 253.

 

 

Answer:16 Option A

 

Explanation:
√29929 = So, √29929 = 173

 

 

Answer:17 Option C

 

Answer:18 Option C

TIME & DISTANCE

by

 

In this module we will deal with basic concepts of time and distance, speed, average speed, conversion from km/h to m/s and vice versa. This chapter will form the basis of further concept of relative speed which is used in train and boat problems.

Important Formulas

  1. Speed=Distance/Time
  2. Distance=Speed×Time
  3. Time=Distance/Speed
  4. To convert Kilometers per Hour(km/hr) to Meters per Second(m/s)
    x km/hr=(x×5)/18m/s
  5. To convert Meters per Second(m/s) to Kilometers per Hour(km/hr)
    x m/s=(x×18)/5 km/hr
  6. If a car covers a certain distance at x kmph and an equal distance at y kmph, the average speed of the whole journey = 2xy/(x+y) kmph
  7. Speed and time are inversely proportional (when distance is constant) ⇒Speed ∝1/Time (when distance is constant)
  8. If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by them to cover the same distance is 1/a:1/b or b : a

Solved Examples

Level 1

1.A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
A. 8.2 B. 4.2
C. 6.1 D. 7.2

 

Answer : Option D

Explanation :

Distance = 600 meter

time = 5 minutes = 5 x 60 seconds = 300 seconds

Speed = distance/time=600/300=2m/s=(2×18)/5 km/hr=36/5 km/hr=7.2 km/hr

2.Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
A. 17 hr B. 14 hr
C. 12 hr D. 19 hr

 

Answer : Option A

Explanation :

Relative speed = 5.5 – 5 = .5 kmph (because they walk in the same direction)

distance = 8.5 km

Time = distance/speed=8.5/.5=17 hr.

3.Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?
A. 1 hr 42 min B. 1 hr
C. 2 hr D. 1 hr 12 min

 

Answer : Option D

Explanation :

New speed = 6/7 of usual speed
Speed and time are inversely proportional.
Hence new time = 7/6 of usual time
Hence, 7/6 of usual time – usual time = 12 minutes
=>1/6 of usual time = 12 minutes => usual time = 12 x 6 = 72 minutes = 1 hour 12 minutes

 4.A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
A. 3 km B. 4 km
C. 5 km D. 6 km

 

Answer : Option D

Explanation :

If a car covers a certain distance at x kmph and an equal distance at y kmph,the average speed of the whole journey = 2xy/(x+y) kmph

Hence, average speed = (2×3×2)/(2+3)=12/5 km/hr .

Total time taken = 5 hours

⇒Distance travelled=(12/5)×5=12 km

⇒Distance between his house and office =12/2=6 km

5.If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
A. 80 km B. 70 km
C. 60 km D. 50 km

 

Answer : Option D

Explanation :

Assume that the person would have covered x km if travelled at 10 km/hr

⇒Speed = Distance/Time=x/10….. (Equation1)

Give that the person would have covered (x + 20) km if travelled at 14 km/hr
⇒Speed = Distance/Time=(x+20)/14….. (Equation2)

From Equations 1 and 2,
X/10=(x+20)/14⇒14x=10x+200⇒4x=200⇒x=200/4=50

6.A car travels at an average of 50 miles per hour for 212 hours and then travels at a speed of 70 miles per hour for 112 hours. How far did the car travel in the entire 4 hours?
A. 210 miles B. 230 miles
C. 250 miles D. 260 miles

 

Answer : Option B

Explanation :

Speed1 = 50 miles/hour

Time1 = 2*(1/2) hour=5/2 hour

⇒Distance1 = Speed1 × Time1 = (50×5)/2=25×5=125 miles

⇒Speed2 = 70 miles/hour

Time2 = 1*1/2 hour=3/2 hour

Distance2 = Speed2 × Time2 = 70×3/2=35×3=105 miles

Total Distance = Distance1 + Distance2 =125+105=230 miles

7.Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
A. 1800 ft B. 2810 ft
C. 3020 ft D. 2420 ft

 

Answer : Option D

Explanation :

Speed of the sound = 1100 ft/s ⇒Time = 11/5 second

Distance = Speed × Time = 1100 ×11/5=220×11=2420 ft

8.A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in meters)?
A. 1250 B. 1280
C. 1320 D. 1340

 

Answer : Option A

Explanation :

Speed = 5 km/hr

Time = 15 minutes = 1/4 hour

Length of the bridge = Distance Travelled by the man

= Speed × Time = 5×1/4 km

=5×1/4×1000 metre=1250 metre

Level 2

1.A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is
A. 11 hrs B. 8 hrs 45 min
C. 7 hrs 45 min D. 9 hts 20 min

 

Answer : Option C

Explanation :

Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back
From this, we can understand that time needed for riding one way = time needed for waking one way – 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
In fact, you can do all these calculations mentally and save a lot of time which will be a real benefit for you.
2.A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
A. 121 km B. 242 km
C. 224 km D. 112 km

 

Answer : Option C

Explanation :

distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 – x) hr
Distance covered in  the first half = 21x
Distance covered in  the second half = 24(10 – x)
But distance covered in  the first half = Distance covered in the second half
=> 21x = 24(10 – x) => 21x = 240 – 24x => 45x = 240 => 9x = 48 => 3x = 16⇒x=16/3

Hence Distance covered in the first half = 21x=21×16/3=7×16=112 km. Total distance = 2×112=224 km

3.A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. What is the actual speed of the car?
A. 30 km/hr B. 35 km/hr
C. 25 km/hr D. 40 km/hr

 

Answer : Option B

Explanation :

Time = 1 hr 40 min 48 sec = 1hr +40/60hr+48/3600hr=1+2/3+1/75=126/75hr

Distance = 42 kmSpeed=distance/time=42(126/75) =42×75/126

⇒5/7 of the actual speed = 42×75/126

⇒actual speed = 42×75/126×7/5=42×15/18=7×15/3=7×5=35 km/hr

4.A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?
A. 36 B. 38
C. 40 D. 42

 

Answer : Option C

Explanation :

Let the distance be x km , the speed in which he moved = v kmph

Time taken when moving at normal speed – time taken when moving 3 kmph faster = 40 minutes

⇒x/v−x/(v+3)=40/60⇒x[1/v−1/(v+3)]=2/3⇒x[(v+3−v)/v(v+3)]=2/3

⇒2v(v+3)=9x…………….(Equation1)

Time taken when moving 2 kmph slower – Time taken when moving at normal speed = 40 minutes
⇒x/(v−2)−x/v=40/60⇒x[1/(v−2)−1/v]=2/3

⇒x[(v−v+2)/v(v−2)]=2/3⇒x[2/v(v−2)]=2/3

⇒x[1/v(v−2)]=1/3⇒v(v−2)=3x…………….(Equation2)

Equation1/Equation2

⇒2(v+3)/(v−2)=3⇒2v+6=3v−6⇒v=12

Substituting this value of v inEquation1⇒2×12×15=9x

=>x= (2×12×15)/9= (2×4×15)/3=2×4×5=40. Hence distance = 40 km

5.In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun’s speed?
A. 8 kmph B. 5 kmph
C. 4 kmph D. 7 kmph

 

Answer : Option B

Explanation :

Let the speed of Arun = x kmph and the speed of Anil = y kmph
distance = 30 km

We know that distance/speed=time. Hence, 30/x−30/y=2………..(Equation1)

30/y−30/2x=1………..(Equation2)

Equation1 + Equation2⇒30/x−30/2x=3⇒30/2x=3⇒15/x=3⇒5/x=1⇒x=5. Hence Arun’s speed = 5 kmph

6.A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
A. 70.24 km/hr B. 74. 24 km/hr
C. 71.11 km/hr D. 72.21 km/hr

 

Answer : Option C

Explanation :

If a car covers a certain distance at x kmph and an equal distance at y kmph,the average speed of the whole journey = 2xy/(x+y) kmph.

By using the same formula, we can find out the average speed quickly average speed = (2×64×80)/(64+80)=(2×64×80)/144⇒ (2×32×40)/36= (2×32×10)/9⇒ (64×10)/9=71.11 kmph

7.A man rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. What is his average speed for the entire trip approximately?
A. 11.2 kmph B. 10 kmph
C. 10.2 kmph D. 10.8 kmph

 

Answer : Option D

Explanation :

Total distance travelled = 10 + 12 = 22 km

Time taken to travel 10 km at an average speed of 12 km/hr = distance/speed=10/12 hr

Time taken to travel 12 km at an average speed of 10 km/hr = distance/speed=12/10 hr

Total time taken =10/12+12/10 hr

Average speed = distance/time=22/(10/12+12/10)=(22×120)/{(10×10)+(12×12)}

(22×120)/244=(11×120)/122=(11×60)/61=660/61≈10.8 kmph

8.An airplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 123 hours, it must travel at a speed of:
A. 660 km/hr B. 680 km/hr
C. 700 km/hr D. 720 km/hr

 

Answer : Option D

Explanation :

Speed and time are inversely proportional ⇒Speed ∝ 1/Time (when distance is constant)

Here distance is constant and Speed and time are inversely proportional

Speed ∝ 1/Time⇒Speed1/Speed2=Time2/Time1

⇒240/Speed2=(1*2/3)5⇒240/Speed2=(5/3)/5⇒240/Speed2=1/3⇒Speed2=240×3=720 km/hr

9.A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car?
A. 80 kmph B. 102 kmph
C. 120 kmph D. 140 kmph

 

Answer : Option C

Explanation :

Let speed of the car = x kmph

Then speed of the train = x *(100+50)/100=150 x /100=3 x /2 kmph

Time taken by the car to travel from A to B=75/x hours

Time taken by the train to travel from A to B=75/(3 x /2)+12.5/60 hours

Since both start from A at the same time and reach point B at the same time

75/x=75/(3 x /2)+12.5/60⇒25/x=12.5/60⇒x=(25×60)/12.5=2×60=120

TIME AND WORK

In these problems the number of persons, quantity of work done and time taken are important factors. Also time taken by a person depends on the efficiency of that person which comes into picture when different people do the work such as women, children do the work alongside the men. The problems related to time and work can be solved by two major approaches – ratio & proportions and unitary method. Let us proceed to find some formulae related to these questions.

Important Formulas – Time and Work

  • If A can do a piece of work in n days, work done by A in 1 day = 1/n

 

  • If A does 1/n work in a day, A can finish the work in n days

 

  • If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then

M1 D1 H1 / W1 = M2 D2 H2 / W2

 

  • If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in pq / (p+q) days

 

  • If A is thrice as good as B in work, then

Ratio of work done by A and B = 3:1

Ratio of time taken to finish a work by A and B = 1: 3

 

SOLVED EXAMPLES

Level 1

1.P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
A. 8/15 B. 7/15
C. 11/15 D. 2/11

 

Answer : Option A

Explanation :

Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15

Fraction of work left = 1 – 7/15= 8/15

2.A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in — hours.
A. 12 hours B. 6 hours
C. 8 hours D. 10 hours

 

Answer : Option A

Explanation :

Work done by A in 1 hour = 1/4

Work done by B and C in 1 hour = 1/3

Work done by A and C in 1 hour = 1/2

Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12

Work done by B in 1 hour = 7/12 – 1/2 = 1/12

=> B alone can complete the work in 12 hours

3.A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
A. 37 ½ days B. 22 days
C. 31 days D. 22 days

 

Answer : Option A

Explanation :

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 — (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 —(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 ½ days

4.P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. How many days does P alone need to finish the remaining work?
A. 8 B. 5
C. 4 D. 6

 

Answer : Option D

Explanation :

Work done by P in 1 day = 1/18

Work done by Q in 1 day = 1/15

Work done by Q in 10 days = 10/15 = 2/3

Remaining work = 1 – 2/3 = 1/3

Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

5.Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
A. 7 hour 15 minutes B. 7 hour 30 minutes
C. 8 hour 15 minutes D. 8 hour 30 minutes

 

Answer : Option C

Explanation :

Pages typed by Anil in 1 hour = 32/6 = 16/3

Pages typed by Suresh in 1 hour = 40/5 = 8

Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3

Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4

= 8 ¼ hours = 8 hour 15 minutes

6.P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in — days
A. 1 B. 2
C. 3 D. 4

 

Answer : Option D

Explanation :

Work done by Q in 1 day = 1/12

Work done by P in 1 day = 2 × (1/12) = 1/6

Work done by P and Q in 1 day = 1/12 + 1/6 = ¼

=> P and Q can finish the work in 4 days

7.A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is
A. 1:3 B. 4:3
C. 2:3 D. 2:1

 

Answer : Option B

Explanation :

Work done by 20 women in 1 day = 1/16

Work done by 1 woman in 1 day = 1/(16×20)

Work done by 16 men in 1 day = 1/15

Work done by 1 man in 1 day = 1/(15×16)

8.P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
A. Rs.40 B. Rs.70
C. Rs.90 D. Rs.100

 

Answer : Option B

Explanation :

Amount Earned by P,Q and R in 1 day = 1620/9 = 180 —(1)

Amount Earned by P and R in 1 day = 600/5 = 120 —(2)

Amount Earned by Q and R in 1 day = 910/7 = 130 —(3)

(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day

– Amount Earned by P,Q and R in 1 day = 120+130-180 = 70

=>Amount Earned by R in 1 day = 70
Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20

= 1/3 :1/4 = 4:3

Level 2

1.P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
A. 10 days B. 14 days
C. 15 days D. 9 days

 

Answer : Option C

Explanation :

Amount of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days

2.A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in – days if they work together.
A. 18 days B. 22 ½ days
C. 24 days D. 26 days

 

Answer : Option B

Explanation :

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=> if the difference is 60 days, B can complete the work in 90 days

=> Amount of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 × (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 22 ½ days

3.P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in
A. 30 days B. 25 days
C. 20 days D. 15 days

 

Answer : Option B

Explanation :

Work done by P and Q in 1 day = 1/10

Work done by R in 1 day = 1/50

Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50

But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day × 2 = 6/50

=> Work done by P in 1 day = 3/50

=> Work done by Q and R in 1 day = 3/50

Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25

So Q alone can do the work in 25 days

4.6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in – days.
A. 4 days B. 6 days
C. 2 days D. 8 days

 

Answer : Option A

Explanation :

Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8b = 1/10

=> 60m + 80b = 1 — (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48b = ½

=> 52m + 96b = 1— (2)

Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200

Work done by 15 men and 20 women in 1 day

= 15/100 + 20/200 =1/4

=> Time taken by 15 men and 20 women in doing the work = 4 days

5.Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?
A. 3 pm B. 2 pm
C. 1:00 pm D. 11 am

 

Answer : Option C

Explanation :

Work done by P in 1 hour = 1/8

Work done by Q in 1 hour = 1/10

Work done by R in 1 hour = 1/12

Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120

Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60

From 9 am to 11 am, all the machines were operating.

Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60.

6.A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in — days.
A. 5 5⁄11 B. 4 5⁄11
C. 6 4⁄11 D. 6 5⁄11

 

Answer : Option A

Explanation :

A can complete the work in 12 days working 8 hours a day

=> Number of hours A can complete the work = 12×8 = 96 hours

=> Work done by A in 1 hour = 1/96

B can complete the work in 8 days working 10 hours a day

=> Number of hours B can complete the work = 8×10 = 80 hours => Work done by B in 1 hour = 1/80

Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480 => A and B can complete the work in 480/11 hours. A and B works 8 hours a day.

Hence total days to complete the work with A and B working together = (480/11)/ (8) = 60/11 days = 5 5⁄11 days

Pending work = 1- 37/60 = 23/60

Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11

which is approximately equal to 2. Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm

7.If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
A. 12 B. 14
C. 16 D. 18

 

Answer : Option C

Explanation :

Wages of 1 woman for 1 day = 21600/(40×30)

Wages of 1 man for 1 day = (21600×2)/(40×30)

Wages of 1 man for 25 days = (21600×2×25)/(40×30)

Number of men = 14400/(21600×2×25)/(40×30)=144/(216×50)/40×30)=144/9=16

8.There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?
A. 3 1⁄4 days B. 4 1⁄3 days
C. 5 1⁄6 days D. 6 1⁄5 days

 

Answer : Option C

Explanation :

Work completed in 1st day = 1/16

Work completed in 2nd day = (1/16) + (1/16) = 2/16

Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16

An easy way to attack such problems is from the choices. You can see the choices are

very close to each other. So just see one by one.

For instance, The first choice given in 3 1⁄4

The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16

The work done in 4 days = (1+2+3+4)/16 = 10/16

The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn’t it?

The work done in 6 days = (1+2+3+4+5+6)/16 > 1

Hence the answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.

(Just for your reference, work done in 5 days = 15/16)

Pending work in 6th day = 1 – 15/16 = 1/16.

In 6th day, 6 people are working and work done = 6/16.

To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.

Hence total time required = 5 + 1/6 = 5 1⁄6 days

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