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?
Answer & explanation
Correct answer: option 2
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