Question

A milk vendor has $2$ cans of milk. The first contains $25\%$ water and the rest milk. The second contains $50\%$ water. How much milk should he mix from each of the containers so as to get $12$liters of milk such that the ratio of water to milk is $3:5?$

Answer 1

Let the cost of 1 liter milk be $Rs.1$

milk in 1 liter mix in 1st can $=\frac{3}{4}l$

C.P. of 1 liter mix in 1st can $=Rs.\frac{3}{4}$

milk in 1 l mix in 2nd can $=\frac{1}{2}l$

C.P of 1 l mix in 2nd can $=Rs.\frac{1}{2}$

milk in 1 l of final mix $=\frac{\frac{3}{4}+\frac{1}{2}}{2}$

$=\frac{\frac{3}{4}+\frac{2}{4}}{2}=5l$

mean price $=5$ rupees.

By rule of alligation, we have

Ref. image

$\therefore$ Ratio of two mixtures $=\frac{1}{8}:\frac{1}{8}=1:1$

So, quantity of mixture taken from each can $=\frac{1}{2}\times 12=6l$