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1. 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

Solution:

Let cost of 1 litre milk be Rs. 1Milk in 1 litre mixture in A =

\frac{8}{13}

litre;
Cost price of 1 litre mixture in A = Rs.

\frac{8}{13}

Milk in 1 litre mixture in B =

\frac{5}{7}

litre;
Cost price of 1 litre mixture in B = Rs.

\frac{5}{7}

Milk in 1 litre of final mixture

\begin{aligned} = \frac{900}{13} \times \frac{1}{100} \times 1 \\ = \frac{9}{13} litre \end{aligned}

Mean price = Rs.

\frac{9}{13}

By the rule of alligation, we have:
Alligation mcq solution image

∴ Required ratio =

\frac{2}{91}

\frac{1}{13}

= 2 : 7

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