The liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?

Correct option is D

Given:
Container 1: Ratio of A : B = 5 : 1 
Container 2: Ratio of A : B = 1 : 3 
Required: Final ratio of A : B = 1 : 1
Solution:
Let x and y be the quantities taken from Container 1 and Container 2 respectively
Amount of A from container 1  $$= x \times \frac{5}{6} \\$$​
Amount of A from container 2$$= y \times \frac{1}{4} \\$$​
​$$\text{Total A} = \frac{5x}{6} + \frac{y}{4} \\$$​
Amount of B from container 1 =$$= x \times \frac{1}{6} \\$$​

Amount of B from container 2 = $$= y \times \frac{3}{4} \\$$​
​$$\text{Total B} = \frac{x}{6} + \frac{3y}{4} \\$$​
Equating A and B to get a 1:1 ratio

$$\frac{5x}{6} + \frac{y}{4} = \frac{x}{6} + \frac{3y}{4} \\\ \\\Rightarrow \frac{5x}{6} - \frac{x}{6} = \frac{3y}{4} - \frac{y}{4} \\\ \\\Rightarrow \frac{4x}{6} = \frac{2y}{4} \\\ \\\Rightarrow \frac{2x}{3} = \frac{y}{2} \\\ \\\Rightarrow 4x = 3y\\ \\ \Rightarrow \frac{x}{y} = \frac{3}{4}$$​