Question : Two pipes, X and Y, can fill a cistern in 24 minutes and 32 minutes, respectively. If both the pipes are opened together, then after how much time (in minutes) should Y be closed so that the tank is full in 18 minutes?
Option 1: 10
Option 2: 8
Option 3: 6
Option 4: 5
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Correct Answer: 8
Solution :
Time taken by X alone to fill the tank = 24 minutes
Part of work done by X alone in a minute = $\frac{1}{24}$
Time taken by Y alone to fill the tank = 32 minutes
Part of work done by Y alone in a minute = $\frac{1}{32}$
Total time taken = 18 minutes
Part of work done by X in 18 minutes = $\frac{18}{24}$ = $\frac{3}{4}$
Work done by Y = 1–$\frac{3}{4}$ = $\frac{1}{4}$
Time taken by Y before it was closed = $\frac{\frac{1}{4}}{\frac{1}{32}}$ = 8 minutes
Hence, the correct answer is 8.
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