Question
Download Solution PDFA cistern is connected to two inlet pipes, A and B, and one outlet pipe, C. Pipe A can fill the cistern in 16 hours, and Pipe B can fill it in 12 hours. Pipe C can drain the entire cistern in 20 hours. If all three pipes are opened at the same time, how long will it take to completely fill the cistern?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Pipe A can fill the cistern in 16 hours
Pipe B can fill the cistern in 12 hours
Pipe C can drain the cistern in 20 hours
Calculation:-
| Pipe | Time (hours) | Total Work | Capacity (units/hour) |
|---|---|---|---|
| A (fills) | 16 | 240 units | 15 |
| B (fills) | 12 | 20 | |
| C (empties) | 20 | -12 |
Let total work be 240 units (LCM of 16, 12, and 20).
Capacity of Pipe A = 240 / 16 = 15 units/hour
Capacity of Pipe B = 240 / 12 = 20 units/hour
Capacity of Pipe C = 240 / 20 = 12 units/hour (since it empties, it's -12)
Net capacity when all three pipes are open = 15 + 20 - 12 = 23 units/hour
Time to fill the tank = 240 / 23 ≈ \(10\frac{10}{23}\) hours
Final Answer: \(10\frac{10}{23}\)hours
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