Question 1

A number increased to 137 1/ 2% gives 33. The number is?

Accepted Answer

∵ 1371/2% of N = 33 ⇒ {(275/2) x N} / 100 = 33 ∴ N = (33 x 2 x 100) / 275 = 24

Question 2

A number decreased to 72 1/ 2% gives 87. The number is?

Accepted Answer

∵ 721/2% of N = 87 ⇒ {(145/2) x N} / 100 = 87 ∴ N = (87 x 2 x 100) / 145 = 120

Question 3

Two numbers are less than a third number by 30%and 37% respectively. How much percent is the second number less than the first?

Accepted Answer

Let third number be N Then, first number = 70% of N = 7N/10 and, Second number = 63% of N = 63N/100 Difference = 7N/10 - 63N/100 = 7N/100 ∴ Required percentage = (7N/100) x (10/7N) x 100 % = 10%

Question 4

In a college election, a candidates secure 62% of the votes and is elected by majority of 144 votes. The total number of votes polled is?

Accepted Answer

∵ (62% of N - 38% of N) =144 ⇒ 24% of N = 144 ∴ N = (144 x 100)/24 = 600

Question 5

The price of sugar is increased by 20%. If the expenditure is not allowed to increased. Then ratio between the reduction in consumption and the original consumption?

Accepted Answer

Reduction in consumption = (20/120) x 100% = 50/3% ∴ Reduction in consumption /Original consumption = (50/3) / 100 = 1/6 = 1 : 6

Question 6

Water tax is increased by 20% but its consumption is decreased by 20%. Then the increase or decrease in the expenditure of the money is?

Accepted Answer

Let tax = Rs. 100 and Consumption = 100 units Original expenditure = Rs. (100 x 100) = 10000 New expenditure = Rs. (120 x 80) = Rs. 9600 ∴ Decreased in expenditure = (400 x 100)/1000 % = 4%

Question 7

3 litres of water is added to 15 litres of a mixture of a 20% solution of alcohol in water. The strength of alcohol is now?

Accepted Answer

Alcohol in 15 litres =(20 x 15)/100 litres = 3 litres Now, alcohol in 18 litres = 3 litres ∴ strength of alcohal =(3/18) x 100 % = 162/3%

Question 8

On deceasing the price of T.V. set by 30%. Its sale in increased by 20%. What is the effect on the revenue received by the shopkeeper?

Accepted Answer

Let price = Rs. 100, sale = 100 Then sale value = Rs. (100 x 100) = Rs. 10000 New sale value = Rs. (70 x 120) = Rs. 8400 Decrease% = (1600/10000) x 100 % = 16%

Question 9

The population of a town is 8000. It increases by 10% during first year and by 20% during the second year. The population after 2 years will be?

Accepted Answer

Population after 2 years =8000(1 + 10/100) (1 + 20/100) = (8000 x 11/10 x 6/5) = 10560

Question 10

A papaya was planted 2 years ago. It increases at the rate of 20% every year. If at present, the height of the tree is 540 cm, what was it when the tree was planted?

Accepted Answer

∵ 540 = H(1 + 20/100)2 ∴ H = (540 x 5/6 x 5/6) = 375 cm

Question 11

The value of a machine depreciates 10% annually. If its present value is Rs. 4000. Its value 2 years later will be?

Accepted Answer

Value of machine 2 years later = Rs. [ 4000 x {(1 - 10)/10)}2] = Rs. (4000 x 9/10 x 9/10) = Rs. 3240

Question 12

The population of a town increase 4% annually but is decreases by emigration annually to the extent of 1/2%. What will be the increase percent in three years?

Accepted Answer

Increase in 3 years over 100 = 100 x {1 + 7/(2 x 100)}3 = (100 x 207/200 x 207/200 x 207/200) = (200 + 7)3 / 80000 = 88869743 / 80000 = 110.8718 Required increase % = (110.8 - 100)% = 10.8%

Question 13

A man's wages were decreased by 50%. Again the reduced wages were increased by 50%. He has a loss of?

Accepted Answer

Let original wages = Rs. 100 Reduced wages = Rs. 50 Increased wages = 150% of Rs. 50 = (150 x 50)/100 = Rs. 75 ∴ Loss = 25%

Question 14

P is six times as large as q. The per cent that q is less than p,is?

Accepted Answer

P = 6q. Thus q is less than p by 5q ∴ q is less than p by = {(6q - q)/6q} x 100% = ( 5q/6q) x 100 % = 831/3 %

Question 15

If A's salary is 30% more than B's then how much per cent is B's salary less than A's?

Accepted Answer

B's salary is less than A's by (30 x 100)/130 % = 231/13%

Question 16

A man spends 75% of his income. This income is increased by 20% and he increased his expenditure by 10%. His savings are increased by?

Accepted Answer

Let income = Rs. 100 Then expenditure = Rs. 75 and saving = Rs. 25 New expenditure = 110% of Rs. 75 = Rs. 165 / 2 New saving = Rs. (120 - 165/2) = Rs. 75/2 Increase in saving = Rs. (75/2 - 25) = Rs. 25/2 ∴ Increase% = (25/2) x (1/25) x 100% = 50%

Question 17

The price of an article has been reduced by 25%. In order to restore the original price, the new price must be increased by?

Accepted Answer

Let original price = Rs. 100 Reduced price = Rs. 75 Increase on Rs. 75 = Rs. 25 Increase on Rs. 100 = (25 x 100)/75 % = 331/3 %

Question 18

If the numerator of a fraction is increased by 20% and he denominator be diminished by 10%, the value of the fraction is 16/21. The original fraction is?

Accepted Answer

Let the original fraction be p/q Now, (120% of p) / (90% of q) = 16 / 21 ⇒ 4p / 3q = 16/21 ∴ p / q = (16/21) x (3/4) = 4 / 7

Question 19

A mixture of 40 litres of milk and water contains 10% water. How much water should be added to this so that water may be 20% in the new mixture?

Accepted Answer

∵ Milk = 90% 0f 40 = 36 litres and water = 4 litres. Let L litre water to be added in order to make 20% water in new mixture. ⇒ {(4 + L) / (40 + L)} x 100 = 20 ⇒ 20 x (40 + L) = 100 x (4 + L) ⇒ 80 x L = 400 ∴ L = 5 litres .

Question 20

The boys and girls in a collage are in ratio 3 : 2. If 20% of the boys and 25% of the girls are adults, the percentage of students who are not adults is?

Accepted Answer

Suppose boys = 3N and girls = 2N Not adults = (80% of 3N) + (75% of 2N) = (12N/5 + 3N/2) = 39N/10 ∴ Required percentage = (39N/10 / 1/5N) x 100 % = 78%

Percentage Questions