The water and milk in two vessels are in the ratio 1:1 and 3:8 respectively. In what ratio, the mixtures in the vessels be mixed to obtain a new mixture containing water and milk in the ratio 4:7?

2:3

The correct answer is Option (2) → 2:3

First vessel: Water = $\frac{1}{2}$, Milk = $\frac{1}{2}$

Second vessel: Water = $\frac{3}{11}$, Milk = $\frac{8}{11}$

Desired mixture: Water = $\frac{4}{11}$, Milk = $\frac{7}{11}$

Let mixtures be mixed in ratio $x:y$.

$\frac{x}{x+y} \cdot \frac{1}{2} + \frac{y}{x+y} \cdot \frac{3}{11} = \frac{4}{11}$

$\frac{x}{2} + \frac{3y}{11} = \frac{4}{11}(x+y)$

$11x + 6y = 8x + 8y$

$3x = 2y \Rightarrow \frac{x}{y} = \frac{2}{3}$

Required ratio = 2:3