Question : Two pipes, A and B, can fill a tank in 36 minutes and 45 minutes, respectively. Another pipe, C, can empty the tank in 30 minutes. Initially, pipes A and B are opened. After 7 minutes, pipe C is also opened. The tank is then filled up in:
Option 1: 39 minutes
Option 2: 46 minutes
Option 3: 40 minutes
Option 4: 45 minutes
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Correct Answer: 46 minutes
Solution :
Time taken by A to fill the tank = 36 minutes
Part of tank filled by A in a minute = $\frac{1}{36}$
Time taken by B to fill the tank = 45 minutes
Part of tank filled by B in a minute = $\frac{1}{45}$
Time taken by C to empty the tank = 30 minutes
Part of tank emptied by C in a minute = $\frac{1}{30}$
Part of the tank filled by A and B in the first 7 minutes = ($\frac{1}{45}$ + $\frac{1}{36}$) × 7
= $\frac{9}{180}$ × 7 = $\frac{7}{20}$
The remaining part of the tank filled by A, B, and C together = 1 – $\frac{7}{20}$ = $\frac{13}{20}$
Part of the tank filled by A, B, and C together in a minute = ($\frac{1}{45}$ + $\frac{1}{36}$) – $\frac{1}{30}$
= $\frac{9 – 6}{180}$ = $\frac{1}{60}$
Time taken to fill the remaining part of tank = $\frac{\frac{13}{20}}{\frac{1}{60}}$ = 39 minutes
Total time taken to fill the tank = 7 + 39 = 46 minutes
Hence, the correct answer is 46 minutes.
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