A mixture contains milk and water in the ratio 8 : x. If 3 litres of water is added in 33 litres of mixture, the ratio of milk and water becomes 2 : 1, then value of x is :

3 Litres

The correct answer is Option (1) → 3 Litres

Since the initial ratio of milk : water is $8 : x$

Milk = $\frac{8}{8+x}×33L$

Water = $\frac{8}{8+x}×33$

After adding 3L of water

Water = $\frac{8}{8+x}×33+3$

Now, $\frac{\text{Milk}}{\text{Water}}=\frac{2}{1}$

$\frac{\frac{8}{8+x}×33}{\frac{8}{8+x}×33+3}=\frac{\frac{8×33}{8+x}}{\frac{33x+24+3x}{6+x}}=\frac{2}{1}$

$\frac{8×33}{33x+24+3x}=\frac{2}{1}$

$8×33=72x+48$

$72x=8×33-48$

$x=\frac{8×33-48}{72}=\frac{216}{72}$

$=3L$