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


1. 3 : 4 
2. 4 : 5
3. 5 : 4 
4. 7 : 8

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Correct Answer - Option 1 : 3 : 4 

Given:

Ratio of water and milk in P is 4 : 5

Ratio of water and milk in Q is 1 : 2

Calculations:

Taking the ratio of water and milk in P and Q in the equal unit,

Ratio of water and milk in P = 4 : 5

Ratio of water and milk in Q = 3 : 6

Ratio of water and milk 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

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