# 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:

75% of the students passed in an examination. If 2 more students had passed the examination, 80% would have been successful. How many students are there in the class?

 A) 40 B) 30 C) 50 D) 32

Explanation:

0 679
Q:

Murali's age 10 years ago was thrice the age of his son Satheesh. Ten years hence, Murali's age will be twice that of Satheesh. The ratio of their present ages is:

 A) 9 : 2 B) 7 : 3 C) 13 : 4 D) 5 : 2

Explanation:

1 673
Q:

The value of a motorcycle depreciates every year by 4%. What will be its value after 2 years, if its present value is ₹75, 000?

 A) ₹69, 120 B) ₹72, 000 C) ₹70, 120 D) ₹69, 000

Explanation:

2 666
Q:

75% of the students passed in an examination. If 2 more students had passed the examination, 80% would have been successful. How many students are there in the class?

 A) 40 B) 30 C) 50 D) 32

Explanation:

0 664
Q:

Sachin’s income is 25% more than Dileep’s income. By how much percentage is Dileep’s income less than Sachin’s income ?

 A) 15% B) 20% C) 18% D) 22%

Explanation:

4 655
Q:

The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?

 A) 10.3 B) 10.7 C) 10.9 D) 9.9

Explanation:

0 654
Q:

62.5% of 4000 is:

 A) 2400 B) 2500 C) 2720 D) 2800

Explanation:

2 654
Q:

In a 15% discount sale, the cost of a book is What was the original price of the book? (Correct to two decimal places)

 A) ₹1, 527.00 B) ₹2, 500.00 C) ₹2, 529.41 D) ₹2, 250.50