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: Jul 15, 2026
- 4 hours
- 4 hours 48 minutes
- 5 hours
- 5 hours 20 minutes
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The Correct Option is B
Approach Solution - 1
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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Approach Solution -2
Three pipes fill or empty a tank at different rates, and we need the time to fill it when all three work together. We can check each option by converting it to a rate and comparing with the combined rate of the three pipes.
- 4 hours: This implies a combined rate of \( \frac{1}{4} \) tank per hour, that is \( \frac{6}{24} \). The actual combined rate is \( \frac{1}{6}+\frac{1}{8}-\frac{1}{12}=\frac{4+3-2}{24}=\frac{5}{24} \), so this does not match.
- 4 hours 48 minutes: This is 4.8 hours, giving a combined rate of \( \frac{1}{4.8}=\frac{5}{24} \) tank per hour, matching the actual combined rate exactly.
- 5 hours: This implies a combined rate of \( \frac{1}{5}=\frac{4.8}{24} \), close to but not equal to \( \frac{5}{24} \), so it does not match.
- 5 hours 20 minutes: This is \( \frac{16}{3} \) hours, giving a combined rate of \( \frac{3}{16}=\frac{4.5}{24} \), which does not match \( \frac{5}{24} \) either.
The combined rate of the three pipes works out to \( \frac{5}{24} \) tank per hour, which corresponds to a fill time of 4 hours 48 minutes.
Therefore, the correct answer is 4 hours 48 minutes.
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Approach Solution -3
Working together, the three pipes fill \( \tfrac{1}{6}+\tfrac{1}{8}-\tfrac{1}{12}=\tfrac{5}{24} \) of the tank every hour. Building up the tank level hour by hour: after hour 1 it is \( 5/24 \) full, after hour 2 it is \( 10/24 \), after hour 3 it is \( 15/24 \), and after hour 4 it is \( 20/24 \), leaving \( 4/24 \) still to fill. We can check each option by seeing whether the tank is exactly full, \( 24/24 \), at that point in time.
- 4 hours: By hour 4 the tank is only \( 20/24 \) full, short of complete by \( 4/24 \).
- 4 hours 48 minutes: This is 4.8 hours; at \( 5/24 \) per hour, the level reached is \( 4.8 \times 5/24=24/24 \), exactly full.
- 5 hours: At \( 5/24 \) per hour, the level reached would be \( 5 \times 5/24=25/24 \), already overflowing past full.
- 5 hours 20 minutes: This is \( 16/3 \) hours; the level reached would be \( \tfrac{16}{3} \times \tfrac{5}{24}=\tfrac{80}{72} \), well past full.
Building up the fill level in steps of \( 5/24 \) each hour shows the tank reaches exactly full only at 4.8 hours, that is 4 hours 48 minutes.
Therefore, the correct answer is 4 hours 48 minutes.
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