A and B are solutions of acid and water. The ratios of water to acid in A and B are 4 : 5 and 1 : 2 respectively. If \(x\) litres of A is mixed with \(y\) litres of B, the ratio of water to acid in the mixture becomes 8 : 13. What is \(x:y\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 : 4
By the rule of alligation on the fraction of water, A and B are taken in the ratio (mean − B’s fraction) : (A’s fraction − mean).
Water in A \(\displaystyle =\frac{4}{9}=\frac{28}{63}\), water in B \(\displaystyle =\frac{1}{3}=\frac{21}{63}\)
Water in the mixture \(\displaystyle =\frac{8}{21}=\frac{24}{63}\)
Share of A \(\propto 24-21=3\)
Share of B \(\propto 28-24=4\)
So \(x:y=\) 3 : 4.