Question

There are two containers: the first contains 500 ml of alcohol, while the second contains 500 ml of water. Three cups of alcohol from the first container is taken out and is mixed well in the second container. Then three cups of this mixture is taken out and is mixed in the first container. Let A denote the proportion of water in the first container and B denote the proportion of alcohol in the second container. Then

• A. A > B
• B. A < B
• C. A = B
• D. Cannot be determined

Hint:

When transferring liquids between two containers in such problems, the total quantities are preserved, and the final proportions are equal.

Answer 1

The Correct Option is C

Initially, the first container has only alcohol, and the second has only water. After transferring the cups as described in the problem, both containers will have some proportion of alcohol and water. The total amount of liquid in both containers remains constant, and the quantities of alcohol and water are just being transferred between the containers. The operations result in a balance between the proportion of alcohol in the first container and the proportion of water in the second container. Therefore, \( A = B \).