The liquids A and B are in the ratio 5:1 in container 1 and 1:3 in container…

Concept

For a mixture of two components, convert each component ratio into a fraction before combining quantities.

If quantities x and y with A-fractions p and q are mixed, the resulting A-fraction is (px + qy)/(x + y). Equating this to the required fraction determines x:y.

Application

1. Let x and y be the amounts taken from containers 1 and 2.

2. Container 1 has A-fraction 5/(5 + 1) = 5/6, and container 2 has A-fraction 1/(1 + 3) = 1/4.

3. The target ratio A:B = 1:1 gives the target A-fraction 1/(1 + 1) = 1/2.

4. Therefore, (5x/6 + y/4)/(x + y) = 1/2.

5. Multiplying by 12(x + y) gives 10x + 3y = 6x + 6y, so 4x = 3y.

6. Hence x:y = 3:4.

Cross-check

For amounts 3 and 4, the amount of A is 3 × 5/6 + 4 × 1/4 = 7/2, while the amount of B is 3 × 1/6 + 4 × 3/4 = 7/2. The amounts are equal, so A:B = 1:1, confirming the mixing ratio 3:4.

Result

The contents of containers 1 and 2 should be mixed in the ratio 3:4.