# 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 sum of the number of male and female students in an institute is 100. If the number of male students is x, then the number of female students becomes x% of the total number of students. Find the number of male students.

 A) 65 B) 50 C) 60 D) 45

Explanation:

1 534
Q:

In a class of 50 students, 60% are boys. The average of marks of the boys is 62, and that of the girls is 68. What is the average marks of the whole class?

 A) 64.8 B) 64.4 C) 65.2 D) 64.6

Explanation:

0 531
Q:

The price of sugar is increased by 17%. A person wants to increase his expenditure by 8% only. By what percent should he decrease his consumption, nearest to one decimal place?

 A) 7.9% B) 8.1% C) 8.3% D) 7.7%

Explanation:

0 528
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 marks obtained by A and B, respectively, are:

 A) 44, 36 B) 40, 32 C) 36, 28 D) 38, 30

Explanation:

6 524
Q:

The price of sugar is increased by 22 % . A person wants to increase his expenditure by 12% only. By what percent should he decrease his consumption, nearest to one decimal place?

 A) 10% B) 8.2% C) 7.8% D) 8.6%

Explanation:

1 519
Q:

An article is sold for Rs.1,680 after two successive discounts of 20% and 16%. What is the marked price of the article?

 A) Rs.2,400 B) Rs.2,500 C) Rs.2,200 D) Rs.2,300

Explanation:

1 516
Q:

A shopkeeper normally allows a discount of 10% on the marked price of each article. During a sale season, he decides to give two more discounts, the first being at a rate of 50% of the original and the second at a rate of 40% of the first. What is the percentage rate of the equivalent single discount (correct up to two decimal places)?

 A) 11.25 B) 13.27 C) 14.85 D) 16.21

Explanation:

0 503
Q:

For a number, greater than one, the difference between itself and its reciprocal is 20% of the sum of it self and its reciprocal. By how much percentage (nearest to an integer) is the square of the number less than its cube?

 A) 122 B) 18 C) 81 D) 33