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 :
Answer & explanation
Correct answer: option 1
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, $\frac{\text{Milk}}{\text{Water}}=\frac{2}{1}$
$\frac{\frac{8}{8+x}×33}{\frac{8}{8+x}×33+3}=\frac{\frac{8×33}{8+x}}{\frac{33x+24+3x}{6+x}}=\frac{2}{1}$
$\frac{8×33}{33x+24+3x}=\frac{2}{1}$
$8×33=72x+48$
$72x=8×33-48$
$x=\frac{8×33-48}{72}=\frac{216}{72}$
$=3L$