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A tank can be filled by a pipe in 15 hours and emptied by another pipe in 20 hou

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Question: A tank can be filled by a pipe in 15 hours and emptied by another pipe in 20 hours. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 10 hours
  2. 12 hours
  3. 15 hours
  4. 18 hours

Correct Answer: 12 hours

Solution: 

The net rate is 1/15 - 1/20 = 4/60 - 3/60 = 1/60. Therefore, it will take 60 hours to fill the tank.

A tank can be filled by a pipe in 15 hours and emptied by another pipe in 20 hou

Practice Questions

Q1
A tank can be filled by a pipe in 15 hours and emptied by another pipe in 20 hours. If both pipes are opened together, how long will it take to fill the tank?
  1. 10 hours
  2. 12 hours
  3. 15 hours
  4. 18 hours

Questions & Step-by-Step Solutions

A tank can be filled by a pipe in 15 hours and emptied by another pipe in 20 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 15 hours, so its rate is 1 tank per 15 hours, or 1/15 of the tank per hour.
  • Step 2: Determine the rate at which the emptying pipe works. It empties the tank in 20 hours, so its rate is 1 tank per 20 hours, or 1/20 of the tank per hour.
  • Step 3: Calculate the net rate when both pipes are open. This is done by subtracting the emptying rate from the filling rate: (1/15) - (1/20).
  • Step 4: To subtract these fractions, find a common denominator. The least common multiple of 15 and 20 is 60.
  • Step 5: Convert the rates to have the same denominator: (1/15) becomes (4/60) and (1/20) becomes (3/60).
  • Step 6: Now subtract the two rates: (4/60) - (3/60) = (1/60). This means the net rate is 1/60 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 divided by (1/60) equals 60 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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