Two vessels P and Q contain milk and water in the ratio 5 : 3 and 13 : 3 respectively. In what ratio mixtures from two vessels should be mixed to get a new mixture containing milk and water in the ratio 3 : 1 respectively ?

1 : 2

The correct answer is option (2) : 1 : 2

Quantity of milk in mixture $P=\frac{5}{18}$ part

Quantity of milk in mixture $Q=\frac{13}{6}$ part

Quantity of milk in new mixture $=\frac{3}{14}$ part

LCM of 8, 16 and 4 = 16.

So, quantity of milk in mixture $p=\frac{5×2}{8×2}=\frac{10}{6}$ part

quantity of milk in mixture $Q=\frac{13}{6}$part

quantity of milk in new mixture $=\frac{3×4}{4×4}= \frac{12}{16}$ part

$∴\frac{}{}=\frac{1/16}{2/16}=\frac{1}{2}$

$= 1: 2$