Question

A vessel is filled with a liquid, 3 parts of which are water and 5parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

• A. $\frac{1}{5}$
• B. $\frac{3}{7}$
• C. $\frac{4}{5}$
• D. $\frac{3}{10}$

Answer 1

The correct option is A $\frac{1}{5}$

Let initially vessel have $8l$ of liquid and $xl$of this liquid be replaced with water then quantity of water in new mixture $=3-\frac{3x}{8}+8$

Quantity of syrup in new mixture $=5-\frac{5x}{8}$

After replacement, the quantity water and syrup same,

So, $3-\frac{3x}{8}+x=5-\frac{5x}{8}$

On solving we get

$x=815$

Ao, the part of mixture replaced

$=\frac{8}{5\times 8}=\frac{1}{5}$