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Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both

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Question: Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 2 hours
  2. 3 hours
  3. 4 hours
  4. 5 hours

Correct Answer: 4 hours

Solution: 

The net rate is 1/6 - 1/4 = -1/12. Therefore, the tank will never fill.

Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both

Practice Questions

Q1
Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both pipes are opened together, how long will it take to fill the tank?
  1. 2 hours
  2. 3 hours
  3. 4 hours
  4. 5 hours

Questions & Step-by-Step Solutions

Pipe A can fill a tank in 6 hours, while pipe B can empty it in 4 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: Tank kabhi nahi bharega.
  • Step 1: Determine the rate at which Pipe A fills the tank. Pipe A can fill the tank in 6 hours, so its rate is 1 tank per 6 hours, or 1/6 of the tank per hour.
  • Step 2: Determine the rate at which Pipe B empties the tank. Pipe B can empty the tank in 4 hours, so its rate is 1 tank per 4 hours, or 1/4 of the tank per hour.
  • Step 3: Calculate the net rate when both pipes are opened together. Since Pipe A fills and Pipe B empties, we subtract Pipe B's rate from Pipe A's rate: 1/6 - 1/4.
  • Step 4: To subtract the fractions, find a common denominator. The common denominator for 6 and 4 is 12.
  • Step 5: Convert the rates to have the common denominator: 1/6 = 2/12 and 1/4 = 3/12.
  • Step 6: Now subtract the rates: 2/12 - 3/12 = -1/12.
  • Step 7: The negative result (-1/12) means that when both pipes are opened together, the tank is actually being emptied at a rate of 1/12 of the tank per hour.
  • Step 8: Since the net rate is negative, the tank will never fill up when both pipes are open.
  • Rate of Work – Understanding how to calculate the rate at which pipes fill or empty a tank.
  • Net Rate Calculation – Combining the rates of filling and emptying to find the overall effect on the tank's water level.
  • Time Calculation – Determining the time taken to fill or empty a tank based on the net rate.
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