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A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 hour

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What’s inside this PDF?

Question: A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 hours. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 10 hours
  2. 5 hours
  3. 15 hours
  4. 20 hours

Correct Answer: 15 hours

Solution: 

The net rate is 1/10 - 1/5 = -1/10. Therefore, the tank will never fill.

A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 hour

Practice Questions

Q1
A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 hours. If both pipes are opened together, how long will it take to fill the tank?
  1. 10 hours
  2. 5 hours
  3. 15 hours
  4. 20 hours

Questions & Step-by-Step Solutions

A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: The tank will never fill.
  • Step 1: Understand that one pipe fills the tank and the other pipe empties it.
  • Step 2: Determine the filling rate of the filling pipe. It fills the tank in 10 hours, so its rate is 1/10 of the tank per hour.
  • Step 3: Determine the emptying rate of the emptying pipe. It empties the tank in 5 hours, so its rate is 1/5 of the tank per hour.
  • Step 4: Calculate the net rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/10) - (1/5).
  • Step 5: Convert 1/5 to a fraction with a denominator of 10: 1/5 = 2/10.
  • Step 6: Now, calculate the net rate: (1/10) - (2/10) = -1/10.
  • Step 7: The negative net rate (-1/10) means that the tank is being emptied faster than it is being filled.
  • Step 8: Conclude that if both pipes are opened together, the tank will never fill.
  • Rate of Work – Understanding how to calculate the rate at which a tank is filled or emptied by different pipes.
  • Combined Rates – Calculating the net effect of multiple rates working together, including filling and emptying.
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