Public finance is the study of the role of the government in the economy. It is the branch of economics which assesses the government revenue and government expenditure of the public authorities and the adjustment of one or the other to achieve desirable effects and avoid undesirable ones.
Fiscal policy relates to raising and expenditure of Money in quantitative and qualitative manner.Fiscal policy is the use of government spending and Taxation to influence the economy. Governments typically use fiscal policy to promote strong and sustainable Growth and reduce POVERTY. The role and objectives of fiscal policy gained prominence during the recent global economic crisis, when governments stepped in to support financial systems, jump-start growth, and mitigate the impact of the crisis on vulnerable groups.
Historically, the prominence of fiscal policy as a policy tool has waxed and waned. Before 1930, an approach of limited government, or laissez-faire, prevailed. With the stock market crash and the Great Depression, policymakers pushed for governments to play a more proactive role in the economy. More recently, countries had scaled back the size and function of government—with markets taking on an enhanced
worldwide Recession, many countries returned to a more active fiscal policy.
How does fiscal policy work?
When policymakers seek to influence the economy, they have two main tools at their disposal—Monetary Policy and fiscal policy. Central banks indirectly target activity by influencing the Money Supply through adjustments to interest rates, bank reserve requirements, and the purchase and sale of Government Securities and Foreign Exchange. Governments influence the economy by changing the level and Types of Taxes, the extent and composition of spending, and the degree and form of borrowing.
Deficit financing, practice in which a government spends more money than it receives as revenue, the difference being made up by borrowing or minting new funds.
Fiscal consolidation is a term that is used to describe the creation of strategies that are aimed at minimizing deficits while also curtailing the accumulation of more debt. The term is most commonly employed when referring to efforts of a local or national government to lower the level of debt carried by the jurisdiction, but can also be applied to the efforts of businesses or even households to reduce debt while simultaneously limiting the generation of new debt obligations. From this perspective, the goal of fiscal consolidation in any setting is to improve financial stability by creating a more desirable financial position.
The public debt is defined as how much a country owes to lenders outside of itself. These can include individuals, businesses and even other governments.public debt is the accumulation of annual budget deficits. It’s the result of years of government leaders spending more than they take in via tax revenues.
A subsidy is a benefit given by the government to groups or individuals usually in the form of a cash payment or tax reduction. The subsidy is usually given to remove some type of burden and is often considered to be in the interest of the public.
Direct Cash Transfer Scheme is a POVERTY reduction measure in which government subsidies and other benefits are given directly to the poor in cash rather than in the form of subsidies.
It can help the government reach out to identified beneficiaries and can plug leakages. Currently, ration shop owners divert subsidised PDS grains or kerosene to open market and make fast buck. Such Leakages could stop. The scheme will also enhance efficiency of welfare schemes.
The https://exam.pscnotes.com/money”>Money is directly transferred into bank accounts of beneficiaries. LPG and kerosene subsidies, pension payments, scholarships and EMPLOYMENT guarantee scheme payments as well as benefits under other government welfare programmes will be made directly to beneficiaries. The money can then be used to buy Services from the market. For eg. if subsidy on LPG or kerosene is abolished and the government still wants
to give the subsidy to the poor, the subsidy portion will be transferred as cash into the banks of the intended beneficiaries.
It is feared that the money may not be used for the intended purpose and men may squander it.
Electronic Benefit Transfer (EBT) has already begun on a pilot basis in Andhra Pradesh, Chhattisgarh, Punjab, Rajasthan, Tamil Nadu, West Bengal, Karnataka, Pondicherry and Sikkim. The government claims the results are encouraging.
Only Aadhar card holders will get cash transfer. As of today, only 21 crore of the 120 crore people have Aadhar cards. Two other drawbacks
are that most BPL families don’t have bank accounts and several villages don’t have any bank branches. These factors can limit the reach of cash transfer.
Sience 1990 ie the Liberalization of Indian economy saw the beginning of Taxation reforms in the nation. The taxation system in the nation has been subjected to consistent and comprehensive reform. Following factors arise the need for TAX REFORMS IN INDIA:-
Tax Resources must be maximized for increased social sector Investment in the economy.
International competitiveness must be imparted to Indian economy in the globalized world.
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-https://exam.pscnotes.com/economic-development”>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 :
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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.
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:
To ensure planning for future by setting up various budgets, the requirements and expected performance of the enterprise are anticipated.
To operate various cost centres and departments with efficiency and economy.
Elimination of wastes and increase in profitability.
Correction of deviations from the established standards.
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.
revenue center (a segment that mainly generates revenue with relatively little costs),
costs for a cost center (a segment that generates costs, but no revenue),
a measure of profitability for a profit center (a segment that generates both revenue and costs) and
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:-
It provides a way to manage an organization that would otherwise be unmanageable.
Assigning responsibility to lower level managers allows higher level managers to pursue other activities such as long term planning and policy making.
It also provides a way to motivate lower level managers and workers.
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 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 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
The process of industrial transition divided into: industrial Growth during the 19th century and industrial progress during the 20th century
Industrial growth during the 19th century
Decline of indigenous industries and the rise of large scale modern industries
1850-55: first https://exam.pscnotes.com/cotton”>Cotton mill, first jute mill and the first coal mine established. RAILWAY also introduced.
Despite some industrialisation, India was becoming an agricultural colony
The thrust to industrialisation came from the British because
They had capital
They had experience in setting up industries in Britain
They had state support
British industrialists were interested in making profits rather than economic growth of India
Parsis, Jews and Americans were also setting industries
No Indian industrialists because
Neither the merchants nor the craftsmen took the lead in setting industries
While the craftsmen didn’t possess capital, the merchants were happy with trading and Money lending activity which was also growing at that time.
However, some Parsis, Gujaratis, Marwaris, Jains and Chettiars joined the ranks of industrialists
Industrial Growth in the first half of the 20th century
Imp events that stimulated industrial growth
1905: Swadeshi Movement
First WW
Second WW
Great stimulus was given to the production of iron and steel, cotton and woollen textiles, leather products, jute.
Tariff protection was given to Indian industries between 1924 and 1939. This led to growth and Indian industrialists were able to capture the market and eliminate foreign completion altogether in important fields
The increase in industrial output between 1939 and 1945 was about 20 percent
After the WW I, the share of the foreign enterprises in India’s major industries began to decline.
Causes for the slow growth of private enterprise in India’s industrialisation
Inadequacy of entrepreneurial ability
Indian industrialists were short-sighted and cared very little for replacement and renovation of machinery
Banking was not highly developed and was more concerned with commerce rather than Industry
Private enterprises and the role of government
Lack of support from the government
Discriminatory tariff policy: one way free-trade
Restrictions transfer of capital equipments and machinery from Britain
Almost all machinery was imported
Despite these difficulties, the Indian indigenous business communities continued to grow, albeit at a slow pace.
Forms and Consequences of Colonial Exploitation
Main forms of colonial exploitation
Exploitation through trade policies
Exploitation through export of British Capital to India
Exploitation through finance capital via the Managing agency system
Exploitation through the payments for the costs of the British administration
Exploitation through trade policies
Exp of cultivators to boost indigo export: forced
Exp of artisans by compulsory procurement by the Company at low prices: gomastas were the agents of the Company who used to do this
Exp through manipulation of export and import duties:
Imports of Indian printed cotton fabrics in England were banned
Heavy import duties on Indian manufactures and very nominal duties on British manufactures.
Discriminating protection was given (to industries that had to face competition from some country other than Britain). This was whittled down, however, by the clause of Imperial Preference under which imports from GB and exports to GB should enjoy the MFN status.
Exploitation through export of British Capital to India
There were three purposes of these investment (in transport and Communication)
To build better access systems for exploited India’s Resources“>Natural Resources
To provide a quick means of communication for maintaining law and order
To provide for quicker disbursal of British manufactures throughout the country and that raw materials
Investments made in machine building, engineering industries and chemicals
Forms of investment
Direct private foreign investment
Sterling loans given to the British Government in India
Estimates show that foreign capital increased from 365 mn sterling in 1911 to 1000 mn sterling in 1933.
British multinationals were the chief instruments of exploitation and it were they who drained out the wealth of India.
These investments show that
British were interested in creating economic infrastructure to aid exploitation and resource drain
They invested in consumer goods and not in basic and heavy industries to prevent the development of Indian industries
Ownership and management of these companies lay in British hands
Exploitation through finance capital via the Managing agency system
Managing agency system: The British merchants who had earlier set up firms acted as pioneers and promoters in several industries like jute, tea and coal. These persons were called managing agents
It may be described as partnerships of companies formed by a group of individuals with strong financial resources and business experience
Functions of managing agents
To float new concerns
Arrange for finance
Act as agents for purchase of raw materials
Act as agents to market the produce
Manage the affairs of the business
They were important because they supplied finance to India when it was starved of capital
In due course, they started dictating the terms of the industry and business and became exploitative and inefficient
They demanded high Percentage of profits. When refused they threatened to withdraw their finance
Exploitation through payments for the costs of British administration
British officers occupied high positions and were paid fabulous remunerations.
Back-to-the-land movement: handicrafts were forced to take up agriculture or become landless labourers. This increased the pressure on land. This trend of growing proportion of the working force on agriculture is described as ‘progressive ruralisation’ or ‘deindustrialisation
of India’. Thus, the crisis in handicrafts and industries seriously crippled Indian agriculture.
Land System during 1793-1850
1793: permanent settlement
Zamindari, Ryotwari, Mahalwari systems
Absentee landlordism emerged
The result of the whole change in the land system led to the emergence of subsistence agriculture
It helped the concentration of economic power in the hand of absentee landlords and moneylenders in rural India.
Commercialisation of Agriculture (1850-1947)
Define: Production of crop for sale rather than for family consumption
What distinguished commercial agriculture from normal sales of marketable surplus was that it was a deliberate policy worked up under the pressure from British industries. It was thus forced upon the Indian peasantry.
Resistance: Indigo revolution etc
Why CA? Industrial Revolution
Impact of railways and road transport: Railways and road transport made possible a huge expansion in cash Cropping, for national and international markets, and production regimes across the subcontinent were placed in a new context of opportunity
Impact of CA
Mass movement to commercial agriculture caused decline in food production, increase in prices and famines.
A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.
Outlet:
A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.
If a pipe can fill a tank in xhours, then:
part filled in 1 hour =
1
.
x
If a pipe can empty a tank in yhours, then:
part emptied in 1 hour =
1
.
y
If a pipe can fill a tank in xhours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then
the net part filled in 1 hour =
1
–
1
.
x
y
If a pipe can fill a tank in xhours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then
the net part emptied in 1 hour =
1
–
1
.
y
x
Questions:
Level-I:
1.
Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
A.
5
11
B.
6
11
C.
7
11
D.
8
11
2.
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
A.
1
13
hours
17
B.
2
8
hours
11
C.
3
9
hours
17
D.
4
1
hours
2
3.
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:
A.
4
1
hours
3
B.
7 hours
C.
8 hours
D.
14 hours
4.
Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
A.
5 min.
B.
9 min.
C.
10 min.
D.
15 min.
5.
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
A.
6 hours
B.
10 hours
C.
15 hours
D.
30 hours
6.
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
A.
60 gallons
B.
100 gallons
C.
120 gallons
D.
180 gallons
7.
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
A.
20 hours
B.
25 hours
C.
35 hours
D.
Cannot be determined
E.
None of these
8.
Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
A.
1 hour
B.
2 hours
C.
6 hours
D.
8 hours
9.
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
A.
12 min
B.
15 min
C.
25 min
D.
50 min
10.
Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
A.
10 min. 20 sec.
B.
11 min. 45 sec.
C.
12 min. 30 sec.
D.
14 min. 40 sec.
11.
Level-II:
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
A.
81 min.
B.
108 min.
C.
144 min.
D.
192 min.
12.
A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
A.
15 min
B.
20 min
C.
27.5 min
D.
30 min
13.
A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
A.
3 hrs 15 min
B.
3 hrs 45 min
C.
4 hrs
D.
4 hrs 15 min
14.
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in:
A.
6 hours
B.
6
2
hours
3
C.
7 hours
D.
7
1
hours
2
15.
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
A.
10
B.
12
C.
14
D.
16
16.
How much time will the leak take to empty the full cistern?
I.
The cistern is normally filled in 9 hours.
II.
It takes one hour more than the usual time to fill the cistern because of la leak in the bottom.
A.
I alone sufficient while II alone not sufficient to answer
B.
II alone sufficient while I alone not sufficient to answer
C.
Either I or II alone sufficient to answer
D.
Both I and II are not sufficient to answer
E.
Both I and II are necessary to answer
17.
How long will it take to empty the tank if both the inlet pipe A and the outlet pipe B are opened simultaneously?
I.
A can fill the tank in 16 minutes.
II.
B can empty the full tank in 8 minutes.
A.
I alone sufficient while II alone not sufficient to answer
B.
II alone sufficient while I alone not sufficient to answer
C.
Either I or II alone sufficient to answer
D.
Both I and II are not sufficient to answer
E.
Both I and II are necessary to answer
18.
If both the pipes are opened, how many hours will be taken to fill the tank?
I.
The capacity of the tank is 400 litres.
II.
The pipe A fills the tank in 4 hours.
III.
The pipe B fills the tank in 6 hours.
A.
Only I and II
B.
Only II and III
C.
All I, II and III
D.
Any two of the three
E.
Even with all the three statements, answer cannot be given.
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.
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
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
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
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
