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?

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: Understanding the Question.
Pipe A fills the tank in 6 hours, Pipe B fills it in 8 hours, and Pipe C, which empties the tank, takes 12 hours to drain a full tank. All three pipes work together, and we need the time to fill the tank.

Step 2: Key Formula or Approach.
We add the filling rates of A and B and subtract the emptying rate of C to get the combined rate, then take the reciprocal to get the time.
\[ \text{Combined rate} = \frac{1}{6} + \frac{1}{8} - \frac{1}{12} \]

Step 3: Detailed Explanation.
Using a common denominator of 24:
\[ \frac{1}{6} = \frac{4}{24}, \quad \frac{1}{8} = \frac{3}{24}, \quad \frac{1}{12} = \frac{2}{24} \]
\[ \text{Combined rate} = \frac{4}{24} + \frac{3}{24} - \frac{2}{24} = \frac{5}{24} \text{ of the tank per hour} \]
The time to fill 1 full tank is the reciprocal of this rate:
\[ \text{Time} = \frac{24}{5} \text{ hours} = 4.8 \text{ hours} \]
Converting the decimal part to minutes: \( 0.8 \times 60 = 48 \) minutes.

Step 4: Final Answer.
The tank fills completely in 4 hours 48 minutes. \[ \boxed{4 \text{ hours } 48 \text{ minutes}} \]
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Approach Solution -2

Instead of working in fractions of the tank, express each pipe's contribution as a percentage of the tank filled or drained per hour. Pipe A fills \( \frac{100}{6}=\frac{50}{3}\% \) per hour, Pipe B fills \( \frac{100}{8}=\frac{25}{2}\% \) per hour, and Pipe C drains \( \frac{100}{12}=\frac{25}{3}\% \) per hour. Together, the net percentage filled per hour is \[ \frac{50}{3}+\frac{25}{2}-\frac{25}{3}=\frac{25}{3}+\frac{25}{2}=\frac{50+75}{6}=\frac{125}{6}\% \] per hour. Reaching 100% then takes \( 100 \div \frac{125}{6}=100\times\frac{6}{125}=4.8 \) hours, which is 4 hours 48 minutes. Test each option by multiplying this net percentage rate by the given time.

  1. Option (A): 4 hours: \( 4\times\frac{125}{6}=\frac{500}{6}\approx83.3\% \) filled, well short of the 100% needed for a full tank.
  2. Option (B): 4 hours 48 minutes: As \( 4.8 \) hours, \( 4.8\times\frac{125}{6}=100\% \), exactly filling the tank.
  3. Option (C): 5 hours: \( 5\times\frac{125}{6}=\frac{625}{6}\approx104.2\% \), meaning the tank would have already overflowed slightly before this point.
  4. Option (D): 5 hours 20 minutes: As \( \frac{16}{3} \) hours, \( \frac{16}{3}\times\frac{125}{6}=\frac{2000}{18}\approx111.1\% \), far beyond what the tank can hold.

Measuring in percentage filled per hour confirms the tank reaches exactly 100% at 4 hours 48 minutes.

Therefore, the correct answer is 4 hours 48 minutes.

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