# 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:

If 15% of x = 20% of y, then x:y is  ___?

 A) 4:3 B) 5:4 C) 4:5 D) 3:4

Explanation:

Given 15% of x = 20% of y

=> 15x = 20y

=> x/y = 20/15

=> x : y = 4 : 3

104 44754
Q:

The ratio 5 : 4 expressed as a percent equals :

 A) 12.5 % B) 40 % C) 80 % D) 125 %

Explanation:

5 : 4 = 5/4 = ( (5/4) x 100 )% = 125%.

169 43682
Q:

270 candidates appeared for an examination, of which 252 passed. The pass percentage is :

 A) (91 + 1/3)% B) (93 + 1/3 )% C) (97 + 1/3 )% D) (98 + 1/3) %

Explanation:

Pass percentage  =[(252/270)*100] % =280/3 % =$9313$ 9 %

127 41083
Q:

1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of the girls pass. The percentage of the total who failed is :

 A) 58 B) 62 *2/3 C) 64 D) 67

Explanation:

Total number of students = 1100 + 700 = 1800.

Number of students passed = (42% of 1100 + 30% of 700) - (462 + 210) = 672.

Number of failues = 1800-672 = 1128.

Percentage failure = (1128/1800 * 100 )% = 62 * 2/3 %.

122 40680
Q:

What will come in place of the question mark(?) in the following question ?

56% of 870 + 82% of 180 = 32% of 90 + ?

 A) 777 B) 666 C) 606 D) 789

Explanation:

56% of 870 = 56x870/100 = 487.20

82% of 180 = 82x180/100 = 147.60

32% of 90 = 32x90/100

487.20 + 147.6 - 28.8  =  ?

? = 634.8  - 28.8

? = 606.

17 40262
Q:

In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 35 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class ?

 A) 25 B) 50 C) 75 D) 100

Explanation:

Let the number of students in the class be 100 and let this required average be x.

Then, (10 * 95) + (20 * 90) + (70 * x) = (100 * 80)

=> 70x = 8000 - (950 + 1800) = 5250

=> x = 75.

133 37604
Q:

What will come in place of the question mark (?) in the following question ?

52.5% of 800 + 30.5% of 2800 = ? + 87.30

 A) 1096.30 B) 1226.70 C) 1124.20 D) 1186.70

Explanation:

52.5% of 800 + 30.5% of 2800 = ? + 87.30

420 + 854 - 87.30 = ?

1274 - 87.30 = ?

? = 1186.70

15 36460
Q:

If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51. What is the original fraction ?

 A) 31/25 B) 15/17 C) 14/25 D) 11/16