Question 1

The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

Accepted Answer

Let the three parts be A, B, C. Then, A : B = 2 : 3 and B : C = 5 : 8 = ❨ 5 x 3 ❩ : ❨ 8 x 3 ❩ = 3 : 24 5 5 5 ⟹ A : B : C = 2 : 3 : 24 = 10 : 15 : 24 5 ⟹ B = ❨ 98 x 15 ❩ = 30. 49

Question 2

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

Accepted Answer

Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x). ⟹ ❨ 120 x 7x ❩ and ❨ 110 x 8x ❩ 100 100 ⟹ 42x and 44x 5 5 ∴ The required ratio = ❨ 42x : 44x ❩ = 21 : 22. 5 5

Question 3

If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?

Accepted Answer

Let 40% of A = 2 B 3 Then, 40A = 2B 100 3 ⟹ 2A = 2B 5 3 ⟹ A = ❨ 2 x 5 ❩ = 5 B 3 2 3 ∴ A : B = 5 : 3.

Question 4

Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

Accepted Answer

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively. Then, 2x + 4000 = 40 3x + 4000 57 ⟹ 57(2x + 4000) = 40(3x + 4000) ⟹ 6x = 68,000 ⟹ 3x = 34,000 Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.

Question 5

If Rs. 782 be divided into three parts, proportional to ½ : ⅔ : ¾, then the first part is:

Accepted Answer

Given ratio = ½ : ⅔ : ¾ = 6 : 8 : 9. ∴ 1st part = Rs. ❨ 782 x 6 ❩ = Rs. 204 23

Question 6

A and B together have Rs. 1210. If 4⁄15 of A's amount is equal to ⅖ of B's amount, how much amount does B have?

Accepted Answer

4 A = 2 B 15 5 ⟹ A = ❨ 2 x 15 ❩B 5 4 ⟹ A = 3 B 2 ⟹ A = 3 B 2 ⟹ A : B = 3 : 2. ∴ B's share = Rs. ❨ 1210 x 2 ❩ = Rs. 484. 5

Question 7

In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

Accepted Answer

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively. Then, sum of their values = Rs. ❨ 25x + 10 x 2x + 5 x 3x ❩ = Rs. 60x 100 100 100 100 ∴ 60x = 30 ⟺ x = 30 x 100 = 50. 100 60 Hence, the number of 5 p coins = (3 x 50) = 150.

Question 8

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

Accepted Answer

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). ⟹ ❨ 140 x 5x ❩ , ❨ 150 x 7x ❩ and ❨ 175 x 8x ❩ 100 100 100 ⟹ 7x, 21x and 14x. 2 ∴ The required ratio = 7x : 21x : 14x 2 ⟹ 14x : 21x : 28x ⟹ 2 : 3 : 4.

Question 9

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

Accepted Answer

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively. Then, 4x - 3x = 1000 ⟹ x = 1000. ∴ B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

Question 10

The fourth proportional to 5, 8, 15 is:

Accepted Answer

Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : 15 : x ⟹ 5x = (8 x 15) x = (8 x 15) = 24. 5

Question 11

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

Accepted Answer

Let the third number be x. Then, first number = 120% of x = 120x = 6x 100 5 Second number = 150% of x = 150x = 3x 100 2 ∴ Ratio of first two numbers = ❨ 6x : 3x ❩ = 12x : 15x = 4 : 5. 5 2

Question 12

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

Accepted Answer

Let A = 2k, B = 3k and C = 5k. A's new salary = 115 of 2k = ❨ 115 x 2k ❩ = 23k 100 100 10 B's new salary = 110 of 3k = ❨ 110 x 3k ❩ = 33k 100 100 10 C's new salary = 120 of 5k = ❨ 120 x 5k ❩ = 6k 100 100 ∴ New ratio ❨ 23k : 33k : 6k ❩ = 23 : 33 : 60 10 10

Question 13

In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

Accepted Answer

Quantity of milk = ❨ 60 x 2 ❩litres = 40 litres. 3 Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres. Then, milk : water = ❨ 40 ❩ . 20 + x Now, ❨ 40 ❩ = 1 20 + x 2 ⟹ 20 + x = 80 ⟹ x = 60. ∴ Quantity of water to be added = 60 litres.

Question 14

If 0.75 : x :: 5 : 8, then x is equal to:

Accepted Answer

(x x 5) = (0.75 x 8) ⟹ x = ❨ 6 ❩ = 1.20 5

Question 15

Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

Accepted Answer

Let the numbers be 3x and 5x. Then, 3x - 9 = 12 5x - 9 23 ⟹ 23(3x - 9) = 12(5x - 9) ⟹ 9x = 99 ⟹ x = 11. ∴ The smaller number = (3 x 11) = 33.

Question 16

Total number of students in a class is 95. if the total number of girls in the class is 45, then the ratio of total number if boys to total number girls is

Accepted Answer

Let the total number of boys in the class be x. Then, according to the question, x + 45 = 95 x = 95 - 45 = 50 Hence, the required ratio of total number of boys to total number of girls = B:G = 50:45 = 10:9

Question 17

The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 490, Krishan has?

Accepted Answer

Ram : Gopal = 7 : 17 = 49 : 119 Gopal : Krishan = 7 : 17 = 119 : 289 ∴ Ram : Gopal : Krishan = 49 : 119 : 289 ⇒ Ram : Krishan = 49 : 289 Thus, 49 : 289 = 490 : N &there N = 289 x 490 / 49 = Rs. 2890

Question 18

The prices of a scooter and a television set are in the ratio 3 : 2. If a scooter costs Rs. 6000 more than the television set, the price of the television set is?

Accepted Answer

Let the price of a scooter be Rs. 3x and that of a television set Rs. 2x. Then, 3x - 2x = 6000 ⇒ x = 6000 ∴ Cost of a television set = 2x = Rs. 12000

Question 19

If 8 : y = y : 18 , then y is equal to?

Accepted Answer

∵ 18 x 18 = y2 ∴ y = √144 = 12

Question 20

A circle and a square have same area. Therefore, the ratio of the side of the square and the radius of the circle is?

Accepted Answer

Let the side of the square be 'a' and let the radius of the circle be 'r' Then, a2 = πr2 ⇒ a2 / r2 = π ⇒ a / r = √π ∴ a : r = √π : 1

Ratio and Proportion Questions