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

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What’s inside this PDF?

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

Options:

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

Correct Answer: 6 hours

Solution: 

The net rate is 1/5 - 1/10 = 1/10. Therefore, it will take 10 hours to fill the tank.

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

Practice Questions

Q1
A tank can be filled by a pipe in 5 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
  1. 3 hours
  2. 4 hours
  3. 5 hours
  4. 6 hours

Questions & Step-by-Step Solutions

A tank can be filled by a pipe in 5 hours and emptied by another pipe in 10 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 10 hours
  • Step 1: Determine 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: Determine 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. Subtract the emptying rate from the filling rate: (1/5) - (1/10).
  • Step 4: To subtract the fractions, find a common denominator. The common denominator for 5 and 10 is 10. Convert 1/5 to 2/10. Now, subtract: 2/10 - 1/10 = 1/10.
  • Step 5: The net rate of filling the tank is 1/10 of the tank per hour. This means it takes 10 hours to fill the entire tank.
  • Rate of Work – Understanding how to calculate the rate at which a tank is filled or emptied by different pipes.
  • Combined Work Rate – Calculating the net effect of multiple processes working together, such as filling and emptying a tank.
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