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 has 60 litres of milk. A removes 4 litres of milk and replaces it with 4 litres of water. Thus, the amount of milk in the mixture is \(60 - 4 = 56\) litres, and the amount of water is 4 litres.

Step 2: B's Sale and Addition of Water.
B sells 30 litres of the mixture. The proportion of milk in the mixture is \( \frac{56}{60} \), and the proportion of water is \( \frac{4}{60} \). In the 30 litres sold, the amount of milk is \( 30 \times \frac{56}{60} = 28 \) litres, and the amount of water is \( 30 \times \frac{4}{60} = 2 \) litres. After selling 30 litres, the remaining mixture has \( 56 - 28 = 28 \) litres of milk and \( 4 - 2 = 2 \) litres of water. B then adds 5 litres of water, making the total water in the mixture \(2 + 5 = 7\) litres.

Step 3: Final Ratio.
The remaining mixture consists of 28 litres of milk and 7 litres of water. Thus, the ratio of milk to water is \( \frac{28}{7} = 4:1 \).

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