Two pipes X and Y can fill a cistern in 24 minutes and 32 minutes, respectively. Both are opened together. After how many minutes should Y be closed so that the tank gets exactly full in a total of 18 minutes?

Introduction / Context:
Let t be the time (minutes) both are open. Then, for the remaining (18 − t) minutes, only X runs. The total work must equal 1 tank. Solve the linear equation for t.

Given Data / Assumptions:

• X rate = 1/24 tank/min.
• Y rate = 1/32 tank/min.
• Total duration = 18 minutes.

Concept / Approach:
Total filled = t*(1/24 + 1/32) + (18 − t)*(1/24) = 1. Solve for t and interpret as the closing time for Y.

Step-by-Step Solution:

Verification / Alternative check:
First 8 minutes: (7/96)*8 = 7/12. Remaining 10 minutes by X: 10/24 = 5/12. Sum = 1.

Why Other Options Are Wrong:
6/10/12 min yield totals not equal to 1 tank in 18 minutes.

Common Pitfalls:
Mixing “when to close Y” with “how long Y runs”—here both are the same t from the start.

Final Answer:
8 min