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When 8 litres of water and 2 litres of alcohol are added to 10 litres of alcohol- water mixture, the ratio of alcohol and water in the mixture becomes 3 ∶ 7. Find the ratio of alcohol and water in the initial mixture.

When 8 litres of water and 2 litres of alcohol are added to 10 litres of alcohol- water mixture, the ratio of alcohol and water in the mixture becomes 3 ∶ 7. Find the ratio of alcohol and water in the initial mixture. Correct Answer 2 ∶ 3

Short trick:

Let the initial mixture be 'W' litre of water and 'A' litre of alcohol.

⇒ W + A = 10      ---- (1)

According to the question,

(A + 2) / (W + 8) = 3/7      ---- (2)

Solving both the equations

⇒ A = 4 and W = 6

∴ Required ratio = 4 ∶ 6 = 2 ∶ 3

Detailed solution:

Let the initial ratio of mixture be ‘x ∶ y’

Amount of alcohol in initial mixture = × 10 = 10x/(x + y)

Amount of water in initial mixture = × 10 = 10y/(x + y)

Now,

Amount of alcohol in new mixture = + 2 = (12x + 2y)/(x + y)

Amount of water in new mixture = + 8 = (8x + 18y)/(x + y)

Ratio of new mixture = ∶ = 3 ∶ 7

⇒ 7(12x + 2y) = 3(8x + 18y)

⇒ 84x + 14y = 24x + 54y

⇒ 84x - 24x = 54y - 14y

⇒ 60x = 40y

⇒ x/y = 40/60 = 2/3

∴ The ratio of initial mixture = 2 ∶ 3

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