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A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 hours. If

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Question: A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 hours. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 4 hours
  2. 5 hours
  3. 6 hours
  4. 7 hours

Correct Answer: 6 hours

Solution: 

The net rate is 1/12 - 1/8 = 1/24. Therefore, it will take 24 hours to fill the tank.

A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 hours. If

Practice Questions

Q1
A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 hours. If both pipes are opened together, how long will it take to fill the tank?
  1. 4 hours
  2. 5 hours
  3. 6 hours
  4. 7 hours

Questions & Step-by-Step Solutions

A pipe can fill a tank in 12 hours, and another pipe can empty it in 8 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 24 hours
  • Step 1: Determine the rate at which the filling pipe works. It can fill the tank in 12 hours, so its rate is 1 tank per 12 hours, or 1/12 of the tank per hour.
  • Step 2: Determine the rate at which the emptying pipe works. It can empty the tank in 8 hours, so its rate is 1 tank per 8 hours, or 1/8 of the tank per hour.
  • Step 3: Calculate the net rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/12) - (1/8).
  • Step 4: To subtract these fractions, find a common denominator. The least common multiple of 12 and 8 is 24.
  • Step 5: Convert the rates to have the common denominator: (1/12) = 2/24 and (1/8) = 3/24.
  • Step 6: Now subtract the two rates: (2/24) - (3/24) = -1/24. This means the tank is being emptied at a rate of 1/24 of the tank per hour.
  • Step 7: Since the net rate is negative, it indicates that the tank is emptying rather than filling. Therefore, it will never fill up if both pipes are open.
  • Rate of Work – Understanding how to calculate the combined rate of filling and emptying a tank using the rates of individual pipes.
  • Net Rate Calculation – Calculating the net effect of two opposing processes (filling and emptying) to determine the overall rate.
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