Vessel A contains milk and water in the ratio 4 : 5. Vessel B contains milk and water in the ratio 2 : 1. If x litres mixture of A is mixed with y litres mixture of B, then the ratio of milk to water in the mixture becomes 8 : 5. Find the ratio x : y.

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Question

This question was previously asked in

SSC CGL 2024 Tier-II Official Paper-I (Held On: 18 Jan, 2025)

Answer 1

Given:

Vessel A contains milk and water in the ratio 4:5.

Vessel B contains milk and water in the ratio 2:1.

If x litres mixture of A is mixed with y litres mixture of B, then the ratio of milk to water in the mixture becomes 8:5.

Formula used:

Milk in A = \(\dfrac{4}{9} \times x\)

Water in A = \(\dfrac{5}{9} \times x\)

Milk in B = \(\dfrac{2}{3} \times y\)

Water in B = \(\dfrac{1}{3} \times y\)

Total Milk/Total Water = \(\dfrac{8}{5}\)

Calculation:

\(\dfrac{\dfrac{4}{9}x + \dfrac{2}{3}y}{\dfrac{5}{9}x + \dfrac{1}{3}y} = \dfrac{8}{5}\)

⇒ \(\dfrac{\dfrac{4x + 6y}{9}}{\dfrac{5x + 3y}{9}} = \dfrac{8}{5}\)

⇒ \(\dfrac{4x + 6y}{5x + 3y} = \dfrac{8}{5}\)

⇒ \((4x + 6y) \times 5 = (5x + 3y) \times 8\)

⇒ \(20x + 30y = 40x + 24y\)

⇒ \(30y - 24y = 40x - 20x\)

⇒ \(6y = 20x\)

⇒ \(y = \dfrac{20}{6}x\) \(= \dfrac{10}{3}x\)

⇒ \(x : y = 3 : 10\)

∴ The correct answer is option (2).

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