Question 1

A, B and C started a business by investing ₹ 28000, ₹ 35000 and ₹ 14000, respectively, At the end of a year, they got a total profit of ₹ 5225. Find A's share?

Accepted Answer

Ratio of shares of A, B and C = Ratio of their investments = 28000 : 35000 : 14000 = 4 : 5 : 2 ∴ A's share = (4/11) x 5225 = ₹ 1900

Question 2

A, B and C started a business by investing ₹ 45000, ₹ 55000 and ₹ 60000, respectively, At the end of the year, they got a total profit of ₹ 11200. Find how much B gets more than A in the profit?

Accepted Answer

Ratio of share of A, B and C = Ratio of their investments = 45000 : 55000 : 60000 = 9 : 11 : 12 A's share = (9/32) x 11200 = ₹ 3150 B's share = (11/32) x 11200 = ₹ 3850 ∴ B's share more than A = ( 3850 - 3150) = ₹ 700

Question 3

If 2A = 3B = 4C then, find A : B : C?

Accepted Answer

Given 2A = 3B = 4C Now 2A = 3B ⇒ A/B = 3/2 or A : B = 3 : 2 = (3 x 2) : (2 : 2) = 6 : 4 Again 3B = 4C ⇒ B/C = 4/3 or B : C = 4 : 3 ∴ A : B : C = 6 : 4 : 3

Question 4

Find the 4th proportional to 4 , 16 and 7 ,

Accepted Answer

Lat the 4th proportional = N Then, 4 : 16 : : 7 : N ⇒ 4/16 = 7/N ⇒ 4N = 7 x 16 ∴ N = (7 x 16)/4 = 7 x 4 = 28

Question 5

What will be the duplicate ratio of 2 : 7?

Accepted Answer

Required duplicate ratio of 2 : 7 = 22 : 72 = 4 : 49

Question 6

Find the sub-duplicate ratio of 81 : 64?

Accepted Answer

Required sub - duplicate ratio of 81 : 64 = √81 : √64 = 9 : 8

Question 7

Find the triplicate ratio of 7 : 5?

Accepted Answer

Required triplicate ratio of 7 : 5 = 73 : 53 = 343 : 125

Question 8

What will be the inverse ratio of 17 : 19?

Accepted Answer

Required inverses ratio of 17 : 19 = (1/17) : (1/19) = 19 : 17

Question 9

If a : b = b : c, then ratio a 4 : b 4 is equal to

Accepted Answer

Given that a /b = b/c ⇒ b2 = ac ∴ a4 : b4 = a4 : a2 c2 = a2 : c2

Question 10

If a : b = 3 : 5 and b : c = 4 : 7 then a : c is equal to

Accepted Answer

Given that, a/b = 3/5, b/c = 4/7 ∴ a/c = a/b x b/c = 3/5 x 4/7 = 12/ 35 &there4: a : c = 12 : 35

Question 11

If 4a = 5b and 7b = 9c, then a : b : c is equal to

Accepted Answer

Given that 4a = 5b ∴ a/b = 5/4 Also 7b = 9c ∴ b/c = 9/7 ∴ a : b = 5 : 4 = (5 x 9) : (4 x 9) = 45 : 36 and b : c = 9 : 7 = (9 x 4) : (7 x 4) = 36 : 28 ∴ a : b : c = 45 : 36 : 28

Question 12

If a/7 = b/9 = c/11, then find a : b : c?

Accepted Answer

Let a/7 = b/9 = c/11 = K Then, a = 7K, b = 9K, c = 11K ∴ a : b : c = 7K : 9K : 11K = 7 : 9 : 11

Question 13

If 30% of A = 20 % of B, then find the value of A : B?

Accepted Answer

Given that, 30 % of A = 20 % of B ⇒ A/B = 20/30 = 2/3 ⇒ A : B = 2 : 3

Question 14

If P : Q : R = 2 : 3 : 4, then find P/Q : Q/R : R/P?

Accepted Answer

Given that, P : Q : R = 2 : 3 : 4 Let P = 2K, Q = 3K, R = 4K ∴ P/Q = 2K/3K = 2/3, Q/R = 3K/4K = 3/4, R/P = 4K/2K = 2/1 ∴ P/Q : Q/R : R/P = 2/3 : 3/4 : 2/1 = (2 x 12)/3 : (3 x 12)/ 4 : (2 x 12)/1 = (2 x 4) : (3 x 3) : 24 = 8 : 9 : 24

Question 15

If A = B/4 and B = C/2, then find the value of A : B : C?

Accepted Answer

Given that, A = B/4 ∴ A/B = 1/4 or A : B = 1 : 4 Also, B = C/2 or B/C = 1/2 or B : C = 1 :2 Now, we have A : B = 1 : 4; B : C = 1 : 2 A : B : C = ( 1 x 1 ) : ( 1 x 4 ) : ( 2 x 4 ) = 1 : 4 : 8

Question 16

If 0.8 x A = 0.09 x B, then find A : B.

Accepted Answer

Given that 0.8 x A = 0.09 x B ⇒ A/B = 0.09/0.8 = 9/80 ∴ A : B = 9 :80

Question 17

If 1/x : 1/y : 1/z = 2 : 3 : 5, then determine x : y : z .

Accepted Answer

Let 1/x = 2K, 1/y = 3K and 1/z = 5K Then, x = K/2, Y = K/3 and z = K/5 ∴ x : y : z = K/2 : K/3 : K/4 = 1/2 : 1/3 : 1/5 = 15 : 10 : 6

Question 18

If a/3 = b/8, then ( a + 3 ) : ( b + 8 ) is equal to?

Accepted Answer

Let a/3 = b/8 = K Then, a = 3K, b = 8K ∴ (a + 3) / (b + 8) = (3K + 3) / (8K + 8) = [3( K + 1)] / [8(K+1)] = 3/8 ∴ ( a + 3 ) : (b + 8) = 3 : 8

Question 19

If 1/2 of A = 2/5 of B = 1/3 of C, then A : B : C is equal to?

Accepted Answer

1/2 of A = 2/5 of B = 1/3 of C 1/2 x A = 2/5 x B = 1/3 x C Let A/2 = 2B/5 = C/3 = K Then, A = 2K, B = 5K/2, C = 3K ⇒ A: B : C = 2k : 5k/2 : 3k ∴ A: B : C = 4 : 5 : 6

Question 20

If xy =36, then which of the following is correct?

Accepted Answer

xy =36 ⇒ xy = 4 x 9, ⇒ x/9 = 4/y ∴ x : 9 = 4 : y

Ratio and Proportion Questions