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 $12$ litres of milk such that the ratio of water to milk is $3:5$?

• A. $4$ litres, $8$ litres
• B. $6$ litres, $6$ litres
• C. $5$ litres, $7$ litres
• D. $7$ litres, $5$ litres

Answer 1

The correct option is B $6$ litres, $6$ litres

Let the cost of $1$ litre milk be Re. $1$
Milk in $1$ litre mix. in $1^{st}$ can $=\frac{3}{4}$ litre, C.P. of $1$ litre mix. in $1^{st}$ can Re. $\frac{3}{4}$
Milk in $1$ litre mix. in $2^{nd}$ can $=\frac{1}{2}$ litre, C.P. of $1$ litre mix. in $2^{nd}$ can Re. $\frac{1}{2}$
Milk in $1$ litre of final mix. $=\frac{5}{8}$ litre, Mean price $=$ Re. $\frac{5}{8}$
By the rule of alligation, we have:
$\therefore$ Ratio of two mixtures $=\frac{1}{8}:\frac{1}{8}=1:1$.
So, quantity of mixture taken from each can $=(\frac{1}{2}\times 12)=6$ litres.