In what ratio must water be mixed with milk to gain $20\%$ by selling the mixture at the cost price of milk?

Question

In what ratio must water be mixed with milk to gain $20\%$ by selling the mixture at the cost price of milk?

Option A

1:4

Option B — Correct answer

1:5

Correct choice.

Option C

1:6

Option D

2:5

Explanation

If milk costs Re 1 per litre and the mixture is sold at Re 1 with a gain of $20\%$, the cost price of 1 litre of mixture must be $\frac{100}{120}=\frac56$. So by alligation between milk at 1 and water at 0 with mean $\frac56$, water : milk $=\frac{1-5/6}{5/6-0}=\frac16:\frac56=1:5$.

Chapter Mock 10: Mixture and Alligation