Question
Download Solution PDFTwo pipes A and C can fill a tank in 10 hours and 15 hours respectively. If A is open all the time and C is open for 30 minutes, then find the time needed for the tank to be filled.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Pipe A fills tank in 10 hours.
Pipe C fills tank in 15 hours.
Pipe C is open for 30 minutes = 0.5 hours
Let Pipe A be open for t hours.
Formula Used:
Work done = Rate x Time
Rate of Pipe A = 1/10 (tank/hour)
Rate of Pipe C = 1/15 (tank/hour)
Calculation:
Part of tank filled by Pipe C in 0.5 hours = (1/15) x 0.5
⇒ Part filled by C = 1/30
Remaining part of tank to be filled by Pipe A = 1 - 1/30
⇒ Remaining part = 29/30
Time taken by Pipe A to fill 29/30 part of tank = (29/30) / (1/10)
⇒ Time for A = (29/30) x 10 = 29/3 hours
Total time needed = Time for A
⇒ Total time = 29/3 hours = \(9\frac{2}{3} \text{ hours}\)
∴ The time needed for the tank to be filled is \(9\frac{2}{3} \text{ hours}\).
Last updated on Jun 2, 2025
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