Discussion

Explanation:

We can solve this by alligation. But while we alligate, we have to be careful that it has to be done with respect to any one of the two liquids, viz. either A or B. We can verify that in both cases, we get the same result. e.g. the proportion of A in the first vessel is $\frac{5}{6}$ and that in the second vessel is $\frac{1}{4},$ and we finally require $\frac{1}{2}$ parts of
A. Similarly, the proportion of B in the first vessel is $\frac{1}{6},$ that in the second vessel is $\frac{3}{4}$ and finally we want it to be $\frac{1}{2}.$ With respect to liquid A

With respect to liquid B

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