# Percentage Questions

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, $\frac{a}{b}=\left(\frac{a}{b}×100\right)%$ .

Thus, $\frac{1}{4}=\left(\frac{1}{4}×100\right)%=25%$

II. If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is $\left[\frac{R}{\left(100+R\right)}×100\right]%$

If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is $\left[\frac{R}{\left(100-R\right)}×100\right]%$

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 = $P{\left(1+\frac{R}{100}\right)}^{n}$

2. Population n years ago =  $\frac{P}{{\left(1+\frac{R}{100}\right)}^{n}}$

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 = $P{\left(1-\frac{R}{100}\right)}^{n}$

2. Value of the machine n years ago = $\frac{P}{{\left(1-\frac{R}{100}\right)}^{n}}$

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

$\left[\frac{R}{\left(100+R\right)}×100\right]%$

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

$\left[\frac{R}{\left(100-R\right)}×100\right]%$

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

Explanation:

3 504
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%

Explanation:

1 498
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

Explanation:

0 488
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

Explanation:

1 470
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

Explanation:

3 447
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

Explanation:

3 429
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

Explanation:

2 419
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