Question

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

• A. \( \frac{2}{3} \)
• B. \( 1 : 2 \)
• C. \( 1 : 3 \)
• D. \( 3 : 4 \)

Hint:

In such proportion problems, first calculate the amount of each substance remaining and then adjust for the added amount.

Answer 1

The Correct Option is B

Initially, there is 80 litres of milk and 20 litres of water. After selling one-fourth, the milk and water sold are: \[ \text{Sold water} = \frac{20}{4} = 5 \quad \text{litres, and similarly, milk sold} = \frac{80}{4} = 20 \quad \text{litres}. \] So, the milk and water remaining are 60 litres of milk and 15 litres of water. To replenish the quantity of water sold, the milkman adds 5 litres of water. Therefore, the new proportion of water to milk is: \[ \frac{15 + 5}{60} = \frac{20}{60} = 1 : 2. \] \[ \boxed{1 : 2} \]