Gnpth wrote:

Two liquids A and B are in the ratio 5:1 in container 1 and in the ratio 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

(E) 1:1

Source: Aristotle.

A in container 1 represents 5/6 of its entire content. In the same way, A represents 1/4 of the content of container 2.

Now we want both A and B to represent each 1/2 of the new container (let's call it H).

So, for container 1 let's call the proportion of liquid A "x" and "y" for the other container, being y = 1 - x

We'll have: 5/6*x + 1/4*(1-x) = 1/2

If you solve it, you'll get: x = 3/7.

This means that liquid A from container 1 will occupy 3/7 of the total amount of liquid A in H. Liquid A from container 2 will occupy 4/7.

The same will happen with liquid B (1/2 * 3/7 + 3/4 * 4/7 = 1/2).

Thus, the asked ratio will be 3:4 (answer D).