FACTS  AND  FORMULAE  FOR  PERCENTAGE  QUESTIONS

 

 

I.Concept of Percentage : By a certain percent , we mean that many hundredths. Thus x percent means x hundredths, written as x%.

To express x% as a fraction : We have , x% = x/100.

Thus, 20% = 20/100 = 1/5;     

48% = 48/100 = 12/25, etc.

To express a/b as a percent : We have, ab=ab×100% .

 

Thus, 14=14×100%=25%

   

 

II. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is R100+R×100%

If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is R100-R×100%

 

 

III. Results on Population : Let the population of the town be P now and suppose it increases at the rate of R% per annum, then :

1. Population after n years = P1+R100n

 

2. Population n years ago =  P1+R100n

 

 

IV. Results on Depreciation : Let the present value of a machine be P. Suppose it depreciates at the rate R% per annum. Then,

1. Value of the machine after n years = P1-R100n

 

2. Value of the machine n years ago = P1-R100n

 

 

V. If A is R% more than B, then B is less than A by

R100+R×100%    

If A is R% less than B , then B is more than A by 

R100-R×100%  

Q:

The price of petrol is increased by 24%. A person wants to increase his expenditure by 14% only. By what percentage (correct to one decimal place), should he decrease his consumption in order to maintain the same level of expenditure ?

 

A) 8.3 B) 7.9
C) 8.1 D) 7.8
 
Answer & Explanation Answer: C) 8.1

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Q:

The given bar graph represents the pass percentage of the 10th and 12th classes of a school during the consecutive four year period 2016-2019.


What is the average of pass percentage of the 10th class for all four years?

 

 

A) 65.25% B) 63.25%
C) 65.75% D) 63.75%
 
Answer & Explanation Answer: D) 63.75%

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Q:

A trader marks his goods in such a way that even after allowing 15% discount on marked price he still gains 27.5%. If the cost price of the goods is ₹ 200, then its marked price is

 

A) 300   B) 250  
C) 350   D) 400  
 
Answer & Explanation Answer: A) 300  

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Q:

A rectangular portion of an airport runway was getting repaired for which an estimate was made on the basis of a rate ₹R per square unit. But while doing the work, the length of the portion got increased by 10% and the breadth by 8%. Over and above this, there was
an increase in the cost of the repair work to the extent of 15%. What was the overall percentage increase in the cost of repair over the estimate?

 

A) 44.14 B) 33
C) 35.24 D) 34.58
 
Answer & Explanation Answer: A) 44.14

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Q:

Two students, A and B, appeared for an examination. A secured 8 marks more than B and the marks of the former was 60% of the sum of their marks. The sum of the marks obtained by A and B is:

 

A) 75 B) 45
C) 40 D) 50
 
Answer & Explanation Answer: C) 40

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Q:

Study the given pie-chart and table carefully and answer the question that follows. The percentage-wise distribution of lecturers in five different subjects in a university is shown in the pie-chart. The total number of lecturers is 500.

Find the number of male lecturers in Physics.

 

 

A) 46 B) 42
C) 44 D) 40
 
Answer & Explanation Answer: C) 44

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Q:

Two students, A and B, appeared for an examination. A secured 8 marks more than B and the marks of the former was 55% of the sum of their marks. The sum of the marks obtained by A and B is:

 

A) 75 B) 100
C) 90 D) 80
 
Answer & Explanation Answer: D) 80

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Q:

If the cost of production doubles in a period of 3 years, then the corresponding maintenance cost in rupees will be

 

A) ₹ 75 lakh B) ₹ 12.5 lakh
C) ₹ 25 lakh D) ₹ 125 lakh
 
Answer & Explanation Answer: C) ₹ 25 lakh

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