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A tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hour

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

Options:

  1. 4 hours
  2. 6 hours
  3. 8 hours
  4. 10 hours

Correct Answer: 4 hours

Solution: 

The net rate is 1/8 - 1/12 = 3/24 - 2/24 = 1/24. Therefore, it will take 24 hours to fill the tank.

A tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hour

Practice Questions

Q1
A tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
  1. 4 hours
  2. 6 hours
  3. 8 hours
  4. 10 hours

Questions & Step-by-Step Solutions

A tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hours. If both pipes are opened together, how long will it take to fill the tank?
  • Step 1: Determine the rate at which the filling pipe works. It fills the tank in 8 hours, so its rate is 1 tank per 8 hours, or 1/8 of the tank per hour.
  • Step 2: Determine the rate at which the emptying pipe works. It empties the tank in 12 hours, so its rate is 1 tank per 12 hours, or 1/12 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: (1/8) - (1/12).
  • Step 4: To subtract these fractions, find a common denominator. The least common multiple of 8 and 12 is 24.
  • Step 5: Convert the rates to have the same denominator: (1/8) = (3/24) and (1/12) = (2/24).
  • Step 6: Now subtract the two rates: (3/24) - (2/24) = (1/24). This means that together, the pipes fill 1/24 of the tank in one hour.
  • Step 7: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 divided by (1/24) equals 24 hours.
  • 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 two pipes working together, one filling and one emptying.
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