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If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hou

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Question: If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hours, how long will it take to fill the tank if both pipes are opened for 2 hours?

Options:

  1. 1 hour
  2. 2 hours
  3. 3 hours
  4. 4 hours

Correct Answer: 3 hours

Solution: 

In 2 hours, the filling pipe fills 2/5 of the tank and the emptying pipe empties 2/10 of the tank. Net filled = 2/5 - 1/5 = 1/5. Therefore, 1/5 of the tank is filled.

If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hou

Practice Questions

Q1
If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hours, how long will it take to fill the tank if both pipes are opened for 2 hours?
  1. 1 hour
  2. 2 hours
  3. 3 hours
  4. 4 hours

Questions & Step-by-Step Solutions

If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hours, how long will it take to fill the tank if both pipes are opened for 2 hours?
  • Step 1: Determine how much of the tank the filling pipe fills in 1 hour. Since it fills the tank in 5 hours, it fills 1/5 of the tank in 1 hour.
  • Step 2: Calculate how much of the tank the filling pipe fills in 2 hours. In 2 hours, it fills 2/5 of the tank (2 * 1/5).
  • Step 3: Determine how much of the tank the emptying pipe empties in 1 hour. Since it empties the tank in 10 hours, it empties 1/10 of the tank in 1 hour.
  • Step 4: Calculate how much of the tank the emptying pipe empties in 2 hours. In 2 hours, it empties 2/10 of the tank, which simplifies to 1/5 of the tank (2/10 = 1/5).
  • Step 5: Find the net amount of the tank filled after 2 hours. Subtract the amount emptied from the amount filled: 2/5 (filled) - 1/5 (emptied) = 1/5 of the tank is filled.
  • Step 6: Since 1/5 of the tank is filled after 2 hours, determine how much time it will take to fill the remaining 4/5 of the tank using the filling pipe alone.
  • Step 7: The filling pipe fills 1/5 of the tank in 1 hour, so to fill 4/5 of the tank, it will take 4 hours (4 * 1 hour).
  • Step 8: Add the 2 hours already spent to the 4 hours needed to fill the remaining part. Total time = 2 hours + 4 hours = 6 hours.
  • Rate of Work – Understanding how to calculate the rate at which pipes fill or empty a tank.
  • Combined Work – Calculating the net effect of multiple processes working simultaneously.
  • Proportional Relationships – Using fractions to represent parts of the tank filled or emptied over time.
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