Question

A mixture of 70 litres of wine and water contains $10\%$ of water. What quantity of water must be added to make the water content $12.5\%$ of the resulting mixture?

• A. 1 litre
• B. 2 litre
• C. 3 litre
• D. 4 litre

Answer 1

The correct option is B

2 litre

Let the required quantity of water to be added be x litres.

Given that 10% of the original mixture is water:-

$\Rightarrow$ Water content in the original mixture $=\frac{10}{100}\times 70=7$ litres

When x litres of water is added, the volume of the solution becomes 70 + x.

The new volume of water = water content in original solution + x

$\Rightarrow$ 7 + x

Given, $7+x=\frac{12.5}{100}\times (70+x)$

$\Rightarrow 700+100x=875+12.5x$

$\Rightarrow 87.5x=175$

$\Rightarrow x=\frac{175}{87.5}=2$

$\therefore$ 2 litres of water must be added to make the water content in the mixture 12.5%.