Question
Download Solution PDFPipe A can fill a tank in 22 hours, and pipe B can fill 50% of the tank in 14 hours. Pipe C can empty the tank in 14 hours. If all the pipes are opened at 5:00 am, and pipe C is closed after 3 hours, then at what time (approx) the tank will be filled?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Pipe A can fill a tank in 22 hours.
Pipe B can fill 50% of the tank in 14 hours.
Pipe C can empty the tank in 14 hours.
Formula Used:
Efficiency = Total work/Time taken
Calculation:
Pipe B can fill full tank = 14 × 2 = 28 hours
Let's assume total work = 308 units (LCM of 22, 28, and 14)
Efficiency of A = 308/22 =14
Efficiency of B = 308/28 =11
Efficiency of C = 308/14 = -22
Now
⇒ Work done by all 3 pipes in 3 hours = {14 + 11 + ( -22)} × 3
⇒ 9 unit
Remaining work = 308 - 9 = 299 units
Time required to fill the remaining tank = 299/ (14+11)
⇒ 11.96 ≈ 12 hours
So,
⇒ 5:00 AM + 3 hours + 12 hours
⇒ 8:00 PM
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