Two vessels A and B contain milk and water in the ratios 8 : 5 and 5 : 2 respectively. In what ratio should the contents of A and B be mixed to get a new mixture containing \(69\frac{3}{13}\)% milk?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2 : 7
By the rule of alligation, the two mixtures are taken in the ratio (B’s strength − mean) : (mean − A’s strength), where strength is the fraction of milk.
Milk in A \(\displaystyle =\frac{8}{13}\), milk in B \(\displaystyle =\frac{5}{7}\)
Mean \(\displaystyle =69\frac{3}{13}\%=\frac{900}{13}\%=\frac{9}{13}\)
B − mean \(\displaystyle =\frac{5}{7}-\frac{9}{13}=\frac{65-63}{91}=\frac{2}{91}\)
Mean − A \(\displaystyle =\frac{9}{13}-\frac{8}{13}=\frac{1}{13}=\frac{7}{91}\)
A : B \(=2:7\)
The vessels must be mixed in the ratio 2 : 7.