Question

Two 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?

• A. 2 : 3
• B. 4 : 3
• C. 3 : 2
• D. 3 : 4

Hint:

When mixing two mixtures, express component quantities using fractional parts and equate based on final ratio conditions.

Answer 1

The Correct Option is B

Let quantities taken from container 1 and 2 be \( x \) and \( y \) respectively.
Container 1 (5:1) ⇒ A = \( \frac{5}{6}x \), B = \( \frac{1}{6}x \)
Container 2 (1:3) ⇒ A = \( \frac{1}{4}y \), B = \( \frac{3}{4}y \) Total A = \( \frac{5x}{6} + \frac{y}{4} \), Total B = \( \frac{x}{6} + \frac{3y}{4} \) Given A : B = 1 : 1, so: \[ \frac{5x}{6} + \frac{y}{4} = \frac{x}{6} + \frac{3y}{4} \] Multiply by 12: \[ 10x + 3y = 2x + 9y \Rightarrow 8x = 6y \Rightarrow \frac{x}{y} = \frac{3}{4} \] So, required ratio = \( x : y = 3 : 4 \Rightarrow \boxed{4 : 3} \)