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?
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
The correct option is (B): 4 hours 48 minutes.
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Approach Solution -2
Pipe A fills the tank in 6 hours, Pipe B fills it in 8 hours, and Pipe C empties it in 12 hours. With all three open together, we need the time to fill the tank. We can check each option by seeing whether the combined work done over that time adds up to exactly 1 full tank.
- Option (A): 4 hours: In 4 hours, the combined fraction filled is \( 4 \times \frac{5}{24} = \frac{20}{24} \), which is only about 0.83 of the tank, not a full tank.
- Option (B): 4 hours 48 minutes: This is \( 4\frac{4}{5} \) hours, or \( \frac{24}{5} \) hours. The combined fraction filled is \( \frac{24}{5} \times \frac{5}{24} = 1 \), which is exactly one full tank.
- Option (C): 5 hours: In 5 hours, the fraction filled is \( 5 \times \frac{5}{24} = \frac{25}{24} \), which is more than a full tank, so this overshoots the actual filling time.
- Option (D): 5 hours 20 minutes: This is \( \frac{16}{3} \) hours, giving a fraction filled of \( \frac{16}{3} \times \frac{5}{24} = \frac{80}{72} \), also more than a full tank, so this too overshoots.
Only 4 hours 48 minutes gives a combined fraction filled of exactly 1, meaning the tank is exactly full at that point.
Therefore, the correct answer is 4 hours 48 minutes.
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Approach Solution -3
Let the tank's capacity be 24 units, chosen as the least common multiple of 6, 8 and 12 so that every pipe's rate comes out as a whole number. Pipe A then fills \( \frac{24}{6}=4 \) units per hour, Pipe B fills \( \frac{24}{8}=3 \) units per hour, and Pipe C drains \( \frac{24}{12}=2 \) units per hour. With all three running together, the net rate is \( 4+3-2=5 \) units per hour, so the tank of 24 units fills in \( \frac{24}{5}=4.8 \) hours, which is 4 hours and 48 minutes. Check this net rate against each option.
- Option (A): 4 hours: In 4 hours at the net rate of 5 units per hour, only \( 4\times5=20 \) units fill, short of the full 24 units, so the tank is not yet full at 4 hours.
- Option (B): 4 hours 48 minutes: This is \( 4.8 \) hours. At 5 units per hour, \( 4.8\times5=24 \) units fill exactly, matching the tank's full 24-unit capacity.
- Option (C): 5 hours: At 5 units per hour for 5 hours, \( 5\times5=25 \) units would fill, one unit more than the tank actually holds, so the tank would already be full slightly before this time.
- Option (D): 5 hours 20 minutes: This is \( \frac{16}{3} \) hours. At 5 units per hour, \( \frac{16}{3}\times5=\frac{80}{3}\approx26.67 \) units, well past the tank's 24-unit capacity.
Working in whole-number capacity units shows the net fill rate is 5 units per hour, and the 24-unit tank fills exactly at 4 hours 48 minutes.
Therefore, the correct answer is 4 hours 48 minutes.
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