Question

A bucket contains milk mixed with water of which $3$ parts are water and $5$ parts are milk. A part of the mixture is removed from the bucket and is replaced by water. What portion of the mixture should have been removed so that the new mixture contains milk and water in equal proportion?

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $\frac{1}{5}$
• D. $\frac{1}{6}$

Answer 1

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

$M=5x$
$W=3x$
Let $y$ part is removed and replaced by water
$\therefore M=5x-\frac{5}{8}y$
$W=3x-\frac{3}{8}y+y$
$M=W$
$\therefore 5x-\frac{5}{8}y=3x-\frac{3}{8}y+y$
$\therefore x=\frac{5}{8}y\Rightarrow y=\frac{8}{5}y$
Required answer $=\frac{\frac{8}{5}x}{8x}=\frac{1}{5}$