Two vessels A and B contain milk and water mixed in the ratio 8 : 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing $69 \frac{3}{13} \%$ milk, is.
A. 2 : 7 B. 3 : 5 C. 5 : 2 D. 5 : 7 Answer: Option AShow Answer
Solution(By Apex Team)
Let cost of 1 litre milk be Rs. 1 Milk in 1 litre mixture in A = $\Large\frac{8}{13}$ litre;
Cost price of 1 litre mixture in A = Rs.$\Large\frac{8}{13}$
Milk in 1 litre mixture in B = $\Large\frac{5}{7}$ litre;
Cost price of 1 litre mixture in B = Rs.$\Large\frac{5}{7}$
Milk in 1 litre of final mixture
$\begin{aligned}&=\frac{900}{13}\times\frac{1}{100}\times1\\
&=\frac{9}{13}\text{ litre }\\
&\text{Mean price = Rs.}\frac{9}{13}\end{aligned}$
By the rule of alligation, we have:
$\begin{aligned}&\text{∴ Required ratio}\\
&=\frac{2}{91}\ :\ \frac{1}{13}\\
&=2\ :\ 7\end{aligned}$
$\begin{aligned}&\text{∴ Required ratio}\\
&=\frac{2}{91}\ :\ \frac{1}{13}\\
&=2\ :\ 7\end{aligned}$
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