Question

A has a container containing 60 litres of pure milk. He takes out 4 litres of milk and replaces it with the same quantity of water. He sells this mixture to B. B sells 30 litres of the mixture and added 5 litres of water in the remaining mixture. The ratio of milk to water in the remaining mixture is:

• A. 5:2
• B. 4:1
• C. 7:2
• D. 3:2

Hint:

When dealing with mixtures, use the concept of proportions to calculate the quantities of ingredients after each step of the process.

Answer 1

The Correct Option is A

Step 1: Initial Mixture Calculation.
Initially, the container holds 60 litres of milk. 4 litres of milk are removed and replaced with 4 litres of water. Consequently, the mixture contains \(60 - 4 = 56\) litres of milk and 4 litres of water.

Step 2: B's Transaction and Water Addition.
B sells 30 litres of the mixture. The proportion of milk in the mixture is \( \frac{56}{60} \), and the proportion of water is \( \frac{4}{60} \). The 30 litres sold contain \( 30 \times \frac{56}{60} = 28 \) litres of milk and \( 30 \times \frac{4}{60} = 2 \) litres of water. Following the sale, the remaining mixture has \( 56 - 28 = 28 \) litres of milk and \( 4 - 2 = 2 \) litres of water. B then adds 5 litres of water, bringing the total water content to \(2 + 5 = 7\) litres.

Step 3: Final Ratio Determination.
The final mixture comprises 28 litres of milk and 7 litres of water. The ratio of milk to water is therefore \( \frac{28}{7} = 4:1 \).

Final Answer: \[ \boxed{5:2} \]