Question:medium

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

Step 1: Assume the tank holds 24 litres, the LCM of 6, 8 and 12. Pipe A fills \( 24 \div 6=4 \) litres per hour, Pipe B fills \( 24 \div 8=3 \) litres per hour, and Pipe C empties \( 24 \div 12=2 \) litres per hour.

Step 2: Working together, the net fill rate is \( 4+3-2=5 \) litres per hour.

Step 3: Time to fill the 24 litre tank is \( \frac{24}{5}=4.8 \) hours, which is 4 hours and \( 0.8 \times 60=48 \) minutes.
\[ \boxed{4 \text{ hours } 48 \text{ minutes}} \]
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Approach Solution -2

Express each pipe's rate as a percentage of the tank filled per hour: Pipe A fills about 16.67 percent per hour, Pipe B about 12.5 percent per hour, and Pipe C drains about 8.33 percent per hour. Combined, the net rate is about \( 16.67+12.5-8.33 \approx 20.83 \) percent per hour. We can check each option by seeing what percentage of the tank would be filled by that time.

  1. 4 hours: At roughly 20.83 percent per hour, 4 hours fills about \( 4 \times 20.83 \approx 83.3\% \), not yet complete.
  2. 4 hours 48 minutes: This is 4.8 hours, filling about \( 4.8 \times 20.83 \approx 100\% \), exactly complete.
  3. 5 hours: This fills about \( 5 \times 20.83 \approx 104.2\% \), already past complete.
  4. 5 hours 20 minutes: This is about 5.33 hours, filling roughly \( 5.33 \times 20.83 \approx 111\% \), well past complete.

At a combined rate of roughly 20.83 percent of the tank per hour, the tank reaches exactly 100 percent full at 4.8 hours, that is 4 hours 48 minutes.

Therefore, the correct answer is 4 hours 48 minutes.

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