Question
Download Solution PDFA pipe can fill a tank in 6 hours, and another pipe can fill the same tank in 8 hours. If both pipes are opened at the same time, how long (in hours, rounded off to one decimal place) will it take to fill the tank?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time taken by the first pipe to fill the tank = 6 hours
Time taken by the second pipe to fill the tank = 8 hours
Both pipes are opened simultaneously.
Formula Used:
Efficiency = Total Work / Time taken
Combined efficiency = Efficiency of first pipe + Efficiency of second pipe
Time taken to fill the tank together = Total Work / Combined efficiency
Calculation:
LCM of 6 and 8 = 24. Let the Total Work (capacity of the tank) = 24 units.
Efficiency of the first pipe = 24 / 6 = 4 units/hour.
Efficiency of the second pipe = 24 / 8 = 3 units/hour.
Combined efficiency when both pipes are open = Efficiency of first pipe + Efficiency of second pipe = 4 + 3 = 7 units/hour.
Time taken to fill the tank together = Total Work / Combined efficiency = 24 / 7 hours.
⇒ 24 ÷ 7 ≈ 3.42857... ≈ 3.4 hours.
It will take approximately 3.4 hours to fill the tank if both pipes are opened at the same time.
Last updated on Jun 2, 2025
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