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A tank has two pipes, one fills it in 5 hours and the other empties it in 10 hou

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Question: A tank has two pipes, one fills it in 5 hours and the other empties it in 10 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 1/5 - 1/10 = 2/10 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.

A tank has two pipes, one fills it in 5 hours and the other empties it in 10 hou

Practice Questions

Q1
A tank has two pipes, one fills it in 5 hours and the other empties it in 10 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

A tank has two pipes, one fills it in 5 hours and the other empties it in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
  • Step 1: Identify the filling rate of the first pipe. It fills the tank in 5 hours, so its rate is 1 tank per 5 hours, or 1/5 of the tank per hour.
  • Step 2: Identify the emptying rate of the second pipe. It empties the tank in 10 hours, so its rate is 1 tank per 10 hours, or 1/10 of the tank per hour.
  • Step 3: Calculate the net rate when both pipes are opened together. The filling rate is 1/5 and the emptying rate is 1/10.
  • Step 4: Convert the rates to a common denominator. The common denominator for 5 and 10 is 10. So, 1/5 becomes 2/10.
  • Step 5: Subtract the emptying rate from the filling rate: 2/10 - 1/10 = 1/10.
  • Step 6: The net rate of filling the tank is 1/10 of the tank per hour.
  • Step 7: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 / (1/10) = 10 hours.
  • 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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