# 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 sugar is increased by 20%. A person wants to increase his expenditure by 8% only. By what percent should he decrease his consumption?

 A) 10% B) 11% C) 9% D) 12%

Explanation:

1 628
Q:

Sham's marks are 25% more than that of Divya's. What percent is Divya's marks less than that of Sham's?

 A) 10% B) 40% C) 20% D) 15%

Explanation:

1 627
Q:

If the length of a rectangle is increased by 40%, and the breadth is decreased by 20%,then the area of the rectangle increases by x%. Then the value of x is:

 A) 16 B) 20 C) 8 D) 12

Explanation:

0 615
Q:

A crate of fruits contains one spoiled fruit for every 25 fruits. 60% of the spoiled fruits were sold. If the seller had sold 48 spoiled fruits, then the number of fruits in the crate were:

 A) 3000 B) 2000 C) 1200 D) 2400

Explanation:

1 606
Q:

Anu fixes the selling price of an article at 25% above its cost of production. If the cost of production goes up by 20% and she raises the selling price by 10%, then her percentage profit is (correct to one decimal place):

 A) 16.4% B) 14.6% C) 13.8% D) 15.2%

Explanation:

0 601
Q:

Ina class of 50 students, 40% are girls. The average marks of the whole class are 64.4 and the average of the boys’ marks is 62. What s the average marks of the girls?

 A) 67 B) 66.8 C) 66.4 D) 68

Explanation:

2 600
Q:

An article was sold at a gain of 16%. If it had been sold for 36 more, the gain would have been 20%. The cost price of the article is

 A) ₹862 B) ₹900 C) ₹810 D) ₹720

Explanation:

3 593
Q:

The price of sugar is increased by 21%. A person wants to increase his expenditure by 12% only. By what percent, correct to one decimalplace, should he reduce his consumption?

 A) 7.6% B) 7.2% C) 7.8% D) 7.4%