Question 1

The total number of students in school is 2140. If the number of girls in the school is 1200, then what is the ratio of the total number of boy to the total number of girls in the school?

Accepted Answer

Number of boy = ( 2140 - 1200 ) = 940 ∴ Boys : Girls = 940 : 1200 = 47 : 60

Question 2

The speed of three cars in the ratio of 2 : 3 : 4 Find the ratio between the time taken by these cars to cover the same distance?

Accepted Answer

Ratio of Speed = 2 : 3 : 4 Ratio of time taken = (1/2) : (1/3) : (1/4) = 6 : 4 : 3

Question 3

If P : Q : = 8 : 15 and Q : R = 3 : 2, then find P : Q : R

Accepted Answer

Given that, P : Q = 8 : 15, Q : R = 3 : 2 P : Q : R = (8 x 3) : (15 x 3) : (15 x 2) = 24 : 45 : 30 ∴ P : Q : R = 8 : 15 : 10 Here, consequent of first ratio should be equal to the antecedent of second ratio.

Question 4

If P : Q = 8 : 15, Q : R = 5 : 8 and R : S = 4 : 5, then P : S is equal to

Accepted Answer

Given, P/Q = 8/15, Q/R = 5/8, R/S = 4/5 ∴ P/S = (P/Q) x (Q/R) x (R/S) ⇒ P/S = (8/15) x (5/8) x (4/5) = 4/15 ∴ P : S = 4 : 15

Question 5

If A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10, then what is A : D equal to?

Accepted Answer

Here, A : B = 2 : 3, B : C = 5 : 7 and C : D = 3 : 10 ∴ A/D = (A/B) x (B/C) x (C/D) = (2/3) x (5/7) x (3/10) = 1/7 ∴ A : D = 1 : 7

Question 6

Calculate the 3rd proportional to 15 and 30.

Accepted Answer

Let the 3rd proportional = k Then, 15 : 30 : : 30 : k ⇒ 15/30 = 30/k ⇒ 15k = 30 x 30 ∴ 15k = 30 x 30 ∴ k = (30 x 30) / 15 = 60

Question 7

Find the mean proportional between 9 and 64.

Accepted Answer

Required mean proportional = √9 x 64 = 3 x 8 = 24

Question 8

If P 2 + 4Q 2 = 4PQ, then determine P : Q.

Accepted Answer

P2 + 4Q2 = 4PQ ⇒ P2 + 4Q2 - 4PQ = 0 ⇒ (P - 2Q)2 = 0 ⇒ P - 2Q = 0 ⇒ P = 2Q ∴ P/Q = 2/1 ∴ P : Q = 2 : 1

Question 9

If P : Q = 7 : 5, then what is the value of (5P - 2Q) : (3P + 2Q)?

Accepted Answer

Given, P/Q = 7/5 ∴ (5P - 2Q) / (3P + 2Q) = (5 x 7 - 2 x 5) / (3 x 7 + 2 x 5) = (35 - 10) / (21 + 10) = 25/31

Question 10

Two number are in the ratio of 4 : 7. If 5 is subtracted from each, the ratio becomes 1 : 2. Find the greater number.

Accepted Answer

Let 1st number be 4k and 2nd number be 7k. According to the question, (4k - 5) / (7k - 5) = 1/2 ⇒ 8k - 10 = 7k - 5 ⇒ 8k - 7k = 10 - 5 ∴ k = 5 ∴ Greater number = 7k = 7 x 5 = 35

Question 11

What sum of money is to divided among 3 persons in the ratio 3 : 4 : 7, so that the second person receives ₹ 12 only?

Accepted Answer

Let required money be ₹ N. Then, (4/14) x N = 12 ⇒ N = (12 x 14)/4 = ₹ 42

Question 12

The price of a scooter and a television are in the ratio of 8 : 7. If a scooter costs ₹ 2000 more than television, then find out the price of television.

Accepted Answer

Let the price of scooter = 8k and price of television = 7k According to the question, 8k - 7k = 2000 ∴ k = 2000 ∴ Price of television = 7k = 7 x 2000 = ₹ 14000

Question 13

The Ratio Between the rates of walking of A and B is 2: 3. If the time taken by B to cover a certain distance is 36 minutes, then time taken by A to cover that much distance is?

Accepted Answer

Ratio of times taken = 1/2: 1/3 1/2 : 1/3 = y : 36 1/3y = 1/2 x 36 y=54 min

Question 14

The sum of three numbers is 68. If the ratio between first and second be 2 : 3 and that between second and third be 5 : 3, then the second number?

Accepted Answer

Let the 3 numbers are a, b, c. Then, a/b = 2/3, b/c = 5/3 ⇒ a/b = (2 x 5) / (3 x 5) = 10/15 and b/c = (5 x 3)/(3 x 3) = 15/9 ⇒ a : b : c = 10 : 15 : 9 Let the number be 10y, 15y and 9y. Then, 10y + 15y + 9y = 68 ⇒ 34y = 68 ⇒ y = 2 ∴ Second number = 15y = 15 x 2 = 30.

Question 15

Three number are in the ratio 3 :4 : 5 . The sum of the largest and the smallest equals the sum of the third and 52. The smallest number is?

Accepted Answer

Let the numbers be 3N, 4N and 5N. Then, 5N + 3N = 4N + 52 ⇒ 4N = 52 ⇒ N = 13 ∴ Then smallest number = 3N = 3 x13 = 39.

Question 16

Rs. 5625 is divided among A, B and C so that A may receive 1/2 as much as B and C together receive and B receives 1/4 of what A and C together receive. The share of A is more than that of B by?

Accepted Answer

∵ A = (B + C)/2 ⇒ B + C = 2 A ⇒ A + B + C = 3A Thus 3A = 5625 ⇒ A = Rs. 1875 Again B = ( A + C )/4 ⇒ A + C = 4B ⇒ A + B + C = 5B ∴ 5B = 5625 ∴ B = Rs. 1125 Thus A's share is more than that of B by Rs. (1875-1125) I.e. Rs. 750.

Question 17

A certain amount was divided between Kavita and Reena in the ratio 4 : 3. If Reena's share was Rs. 2400. The amount is?

Accepted Answer

Let their shares be Rs. 4x and Rs. 3x. Then 3x = 2400 ⇒ x = 800 ∴ Total amount = 7x = Rs. 5600

Question 18

A, B and C can do a work in 20, 25 and 30 days respectively. They undertook to finish the work together for Rs. 2220, then the share of A exceeds that of B by?

Accepted Answer

Ratio of shares of A, B and C = 1/20 : 1/25 : 1/30 = 15 : 12 : 10 ∴ A's share = Rs.(2220 x 15/37) = Rs. 900 B's share = Rs.(2220 x 12/37) =Rs. 720 Thus, the share of A exceeds that of B by Rs.(900 - 720) = Rs. 180.

Question 19

The monthly salary of A, B, C is in the proportion of 2 : 3 : 5. If c's monthly salary is Rs. 1200 more than that of A, then B's annual salary is?

Accepted Answer

Let the monthly salary of A, B, C be Rs. 2x, Rs.3x and Rs. 5x respectively. Then, 5x - 2x = 1200 ∴ x = 400 ∴ B's monthly salary = 3x = Rs. 1200 Hence, B's annual salary = Rs. (12 x 1200)= Rs. 14400

Question 20

A bag contains 25 paise,10 paise and 5 paise coins in the ratio 1 : 2 : 3. If their total value is Rs. 30, the number of 5 paise coins is?

Accepted Answer

Ratio of their values = 1/4 : 2/10 : 3/20 = 5 : 4 : 3 ∴ Value of 5 paise coins =Rs. (30 x 3/12) = Rs. 7.50 ∴ Number of 5 paise coins = 750/5 = 150

Ratio and Proportion Questions