Question

A and B are solutions of acid and water. The ratios of water and acid in A and B are 4 : 5 and 1 : 2 respectively. If x liters of A is mixed with y liters of B, then the ratio of water and acid in the mixture becomes 8 : 13 What is x : y?
1. 5 : 6
2. 3 : 4
3. 2 : 3
4. 2 : 5

Answer 1

Correct Answer - Option 2 : 3 : 4

Given:

Ratio of water and acid in A = 4 ∶ 5

Ratio of water and acid in B = 1 ∶ 2

Calculations:

Taking the ratio of water and acid in A and B in the equal unit,

Ratio of water and acid in A = 4 ∶ 5

Ratio of water and acid in B = 3 ∶ 6

Ratio of water and acid in the mixture = (4x + 3y)/(5x + 6y)

⇒ (4x + 3y)/(5x + 6y) = 8/13

⇒ 52x + 39y = 40x + 48y

⇒ 12x = 9y

⇒ x/y = 9/12

⇒ x/y = 3/4

∴ The ratio of x and y is 3 ∶ 4