###
**A vessel is filled with liquid, 3 parts of which are water and 5 parts 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. $\large\frac{1}{3}$
B. $\large\frac{1}{4}$
C. $\large\frac{1}{5}$
D. $\large\frac{1}{7}$
**Answer: Option C**

## Show Answer

Solution(By Apex Team)

Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
Quantity of water in new mixture = $\left(3-\Large\frac{3 x}{8}+x\right)$ litres
Quantity of syrup in new mixture = $\left(5-\Large\frac{5 x}{8}\right)$ litres
$\begin{aligned}&\therefore3-\frac{3x}{8}+x=5-\frac{5x}{8}\\
&\Rightarrow5x+24=40-5x\\
&\Rightarrow10x=16\\
&\Rightarrow x=\frac{8}{5}\end{aligned}$
So, part of the mixture replaced
$\begin{array}{l}
=\Large\frac{8}{5} \times \frac{1}{8} \\
=\Large\frac{1}{5}
\end{array}$

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