Question

A cask contains a mixture of $49litres$ of wine and water in the ratio $5:2$. How much water must be added to it so that the ratio of wine to water is $7:4$?

• A. $3.5litres$
• B. $7litres$
• C. $4litres$
• D. $6litres$

Answer 1

The correct option is D $6litres$

The ratio of wine and water $=5:2$

Total mixture $=49litres$

Then, the share of wine is $=\frac{5\times 49}{7}=35litres$

And, of water $=\frac{2\times 49}{7}=14litres$

Let $x$ litres of water be added in new mixture, then ratio $=35:(14+x)$

It is given that the ratio of wine and water in the new mixture is $7:4$

$\therefore \frac{35}{14+x}=\frac{7}{4}$

$\Rightarrow 98+7x=140\Rightarrow 7x=42$

$\therefore x=6litres$

Hence, option D is the correct answer.