Question:
A tank is connected to three pipes – Pipe A, B and C. Pipe A can fill the tank in 6 hours, B can fill the tank in 8 hours and Pipe C can empty the full tank in 12 hours. How much time will it take to fill the tank completely if all three pipes are working together?
A tank is connected to three pipes – Pipe A, B and C. Pipe A can fill the tank in 6 hours, B can fill the tank in 8 hours and Pipe C can empty the full tank in 12 hours. How much time will it take to fill the tank completely if all three pipes are working together?
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Inlet rates are positive, outlet (emptying) rates negative. Sum the rates, then invert to get the time.
Updated On: Aug 13, 2025
- 4 hours
- 4 hours 48 minutes
- 5 hours
- 5 hours 20 minutes
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The Correct Option is B
Solution and Explanation
Rates: A fills $\tfrac{1}{6}$ tank/hr, B fills $\tfrac{1}{8}$ tank/hr, C empties $\tfrac{1}{12}$ tank/hr.
Net rate: \[ \frac{1}{6}+\frac{1}{8}-\frac{1}{12} = \frac{4}{24}+\frac{3}{24}-\frac{2}{24} = \frac{5}{24}\ \text{tank/hr}. \] Time to fill $= \dfrac{1}{\text{rate}}= \dfrac{24}{5}$ hours $= 4.8$ hours $= 4$ hours $48$ minutes.
Net rate: \[ \frac{1}{6}+\frac{1}{8}-\frac{1}{12} = \frac{4}{24}+\frac{3}{24}-\frac{2}{24} = \frac{5}{24}\ \text{tank/hr}. \] Time to fill $= \dfrac{1}{\text{rate}}= \dfrac{24}{5}$ hours $= 4.8$ hours $= 4$ hours $48$ minutes.
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