Question 44
The milk and water in two vessels P and Q are in the ratio 5:2 and 2:3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel R containing milk and Half water?
Solution
The concentration of milk in vessel P = 5/7and in vessel Q = 2/5.
We need to mix them in such a way so that we get a solution with milk's concentration = 1/2.
Using alligation cross method:
5/7 2/5
1/2
The ratio we get = $$\frac{\frac{1}{2}-\frac{2}{5}}{\frac{5}{7}-\frac{1}{2}}=\frac{\frac{1}{10}}{\frac{3}{14}}=\frac{7}{15}$$.
Thus, the ratio in which the solutions are mixed is 7:15.
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