# 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:

A shopkeeper marks the price of the article in such a way that after allowing 28% discount, he wants a gain of 12%. If the marked price is ₹224. then the cost price of the article is:

 A) ₹168 B) ₹144 C) ₹120 D) ₹196

Explanation:

0 523
Q:

The price of sugar is increased by 24%. A person wants to increase his expenditure by 15% only. By what percentage, correct to one decimal place, should he reduce his consumption?

 A) 7.1 B) 7.3 C) 6.9 D) 7.5

Explanation:

2 516
Q:

The price of sugar is increased by 18%. A person wants to increase the expenditure by 12% only. By what percent, correct to one decimalplace, should he decrease his consumption?

 A) 5.6% B) 5.1% C) 6% D) 5.3%

Explanation:

1 508
Q:

Each side of a rectangular field is increased by 10%. Then the percentage increase in the area of the field is:

 A) 21% B) 10% C) 18% D) 15%

Explanation:

0 500
Q:

The price of sugar is increased by 17%. A person wants to increase his expenditure by 7% only. By what percentage, correct to one decimal place, should he reduce his consumption?

 A) 8.3% B) 8.1% C) 8.7% D) 8.5%

Explanation:

0 497
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:

0 494
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:

1 492
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