Question 1

What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

Accepted Answer

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such number =14 ∴ Required percentage = ❨ 14 x 100 ❩% = 20%. 70

Question 2

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

Accepted Answer

Number of valid votes = 80% of 7500 = 6000. ∴ Valid votes polled by other candidate = 45% of 6000 = ❨ 45 x 6000 ❩ = 2700. 100

Question 3

Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

Accepted Answer

5% of A + 4% of B = 2 (6% of A + 8% of B) 3 ⟹ 5 A + 4 B = 2 ❨ 6 A + 8 B ❩ 100 100 3 100 100 ⟹ 1 A + 1 B = 1 A + 4 B 20 25 25 75 ⟹ ❨ 1 - 1 ❩ A = ❨ 4 - 1 ❩ B 20 25 75 25 ⟹ 1 A = 1 B 100 75 A = 100 = 4 . B 75 3 ∴ Required ratio = 4 : 3

Question 4

Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?

Accepted Answer

Let the amount taxable purchases be Rs. x . Then, 6% of x = 30 100 ⟹ x = ❨ 30 x 100 ❩ = 5. 100 6 ∴ Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70

Question 5

A student multiplied a number by 3⁄5 instead of 5⁄3. What is the percentage error in the calculation?

Accepted Answer

Let the number be x. Then, error = 5 x - 3 x = 16 x. 3 5 15 Error% = ❨ 16x x 3 x 100 ❩% = 64%. 15 5x

Question 6

A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?

Accepted Answer

Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 110 - (60) = 50. ∴ Required percentage = ❨ 50 x 100 ❩% = 45 5 % 110 11

Question 7

Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?

Accepted Answer

Let the sum paid to Y per week be Rs. z . Then, z + 120% of z = 550. ⟹ z + 120 z = 550 100 ⟹ 11 z = 550 5 ⟹ z = ❨ 550 x 5 ❩ = 250. 11

Question 8

Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

Accepted Answer

Let their marks be ( x + 9) and x . Then, x + 9 = 56 (x + 9 + x) 100 ⟹ 25(x + 9) = 14(2x + 9) ⟹ 3x = 99 ⟹ x = 33 So, their marks are 42 and 33.

Question 9

Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.

Accepted Answer

Rebate = 6% of Rs. 6650 = Rs. ❨ 6 x 6650 ❩ = Rs. 399. 100 Sales tax = 10% of Rs. (6650 - 399) = Rs. ❨ 10 x 6251 ❩ = Rs. 625.10 100 ∴ Final amount = Rs. (6251 + 625.10) = Rs. 6876.10

Question 10

If 20% of a = b, then b% of 20 is the same as:

Accepted Answer

20% of a = b ⟹ 20 a = b. 100 ∴ b% of 20 = ❨ b x 20 ❩ = ❨ 20 a x 1 x 20 ❩ = 4 a = 4% of a. 100 100 100 100

Question 11

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

Accepted Answer

Suppose originally he had x apples. Then, (100 - 40)% of x = 420. ⟹ 60 x x = 420 100 ⟹ x = ❨ 420 x 100 ❩ = 700. 60

Question 12

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is ⅔ of the number of students of 8 years of age which is 48. What is the total number of students in the school?

Accepted Answer

Let the number of students be x . Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. ∴ 80% of x = 48 + 2 of 48 3 ⟹ 80 x = 80 100 ⟹ x = 100.

Question 13

If A = x% of y and B = y% of x, then which of the following is true?

Accepted Answer

x% of y = ❨ x x y ❩ = ❨ y x x ❩ = y% of x 100 100 ∴ A = B.

Question 14

Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

Accepted Answer

Total number of votes polled = (1136 + 7636 + 11628) = 20400. ∴ Required percentage = ❨ 11628 x 100 ❩% = 57%. 20400

Question 15

The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

Accepted Answer

Increase in 10 years = (262500 - 175000) = 87500. Increase% = ❨ 87500 x 100 ❩% = 50%. 175000 ∴ Required average = ❨ 50 ❩% = 5%. 10

Question 16

The selling price and cost price of an article differs by 480. What is the selling price in case the profit percentage is 20%?

Accepted Answer

SP - CP = 480 1.2x - x = 480 ⇒0.2x = 480 ⇒x = 2400

Question 17

If a person sells a wooden furniture at 8% profit against 8% loss, then he could had earned Rs12 more. What is the cost price of furniture?

Accepted Answer

Let Cost Price (CP) = x Then Selling Price(SP) if he sells at profit = x(1+8%) = 1.08x and SP, if he sells at loss = x(1-8%) = 0.92% Given, 1.08%-0.92% = Rs12 0.16x = Rs.12 ⇒x = Rs.75

Question 18

Calculate the amount of water which should be added to 80% solution of Sulphuric acid to make it a 50% solution?

Accepted Answer

Concentration of Sulphuric acid = 80% So in a 100cc, Sulphuric acid = 80cc and water = 20cc Let x be the amount of water added to make concentration of 50% ⇒80/(100+x) = 50/100 ⇒ 80/(100+x) = 1/2 ∴ x = 60cc

Question 19

An metallic alloy contains 20g copper, 20g tin and 40g silver.Then find out the percentage of tin in the alloy?

Accepted Answer

Total weight of alloy = 20+20+ 40 = 80g Weight of tin = 20g Percentage of tin = 20g/80g x 100 =25%

Question 20

If the price of petrol is increased by 20% and subsequently by 40%. If the original price was Rs25 per litre then what is then the final price per litre?

Accepted Answer

Final Price = 25 x (1 + 20/100) x (1 + 40/100) =Rs.25 x 1.2 x 1.4 = Rs. 42

Percentage Questions