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.
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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
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Solution

 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 $=8 x$

$$

\begin{array}{l}

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

\text { itres; Ans. }

\end{array}

$$

Correct option $=(\mathrm{d})$

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

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