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1. A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is -

A. 3 litres

B. 4 litres

C. 15 litres

D. 10 litres

Solution:

Let the quantity of alcohol and water be 4x litres and 3x litres respectively

\begin{aligned} \frac{4 x}{(3 x + 5)} = \frac{4}{5} \\ \Rightarrow 20 x = 4 (3 x + 5) \\ \Rightarrow 8 x = 20 \\ \Rightarrow x = 2.5 \end{aligned}

Quantity of alcohol
= (4 × 2.5) litres
= 10 litres.

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