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1. Two vessels A and B contain spirit and water mixed in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5 ?

A. 4 : 3

B. 3 : 4

C. 5 : 6

D. 7 : 9

Solution:

Let the Cost price of spirit be Rs. 1 per litre
Spirit in 1 litre mixture in A =

\frac{5}{7}

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

\frac{5}{7}

Spirit in 1 litre mixture of B =

\frac{7}{13}

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

\frac{7}{13}

Spirit in 1 litre mixture of C =

\frac{8}{13}

litre;
Mean price = Rs.

\frac{8}{13}

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

∴ Request ratio =

\frac{1}{13}

\frac{9}{91}

= 7 : 9

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