Question

A mixture of 70 litres of wine and water contains $10\%$ water. How much 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 = x litres.

Given that 10% of the original wine is water.

$\Rightarrow$ Water content in wine $=\frac{10}{100}\times 70=7$

When x litres of water is added, volume of solution = 70 + x

New volume of water = water content in original solution + x

= 7 + x

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

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

$\Rightarrow 87.5x=175$

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

2 litres of water must be added to make the mixture contain 12.5% of water