Question

In a mixture, the ratio of milk and water is $8: 7$. If 11 litres of water is mixed, then the ratio becomes $8: 9$. Find the amount of milk in the initial mixture.

(A) 63 litres

(B) 88 litres

(C) 22 litres

(D) 44 litres

Answer 1

Let the amounts of milk and water are $8 x$ and $7 x$.

$
\begin{array}{l}
\therefore \quad \frac{8 x}{7 x+11}=\frac{8}{9} \\
\Rightarrow \quad 72 x=56 x+88 \\
\Rightarrow \quad 72 x-56 x=88 \\
\Rightarrow \quad 16 x=88 \\
\therefore \quad x=\frac{88}{16}
\end{array}
$

$\therefore$ The amount of milk $=8 x$

$=8 \times \frac{88}{16}$

$=$ 44 Litres; Ans.

Correct option $=(D)$

Trick :

Milk: Water

$
\begin{aligned}
8: & 7 \\
8: & 9 \\
\hline & 2=11
\end{aligned}
$

$\therefore$ Amount of milk $=\frac{11}{2} \times 8$

$=44$ litres: Ans