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A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours

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Question: A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours. If both pipes are opened together, how long will it take to fill the tank? (2020)

Options:

  1. 12 hours
  2. 24 hours
  3. 48 hours
  4. 18 hours

Correct Answer: 12 hours

Exam Year: 2020

Solution: 

Rate of filling = 1/6 tank/hour, Rate of emptying = 1/8 tank/hour. Combined rate = 1/6 - 1/8 = 1/24 tank/hour. Time = 1 / (1/24) = 24 hours.

A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours

Practice Questions

Q1
A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours. If both pipes are opened together, how long will it take to fill the tank? (2020)
  1. 12 hours
  2. 24 hours
  3. 48 hours
  4. 18 hours

Questions & Step-by-Step Solutions

A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours. If both pipes are opened together, how long will it take to fill the tank? (2020)
  • Step 1: Determine the rate at which the filling pipe works. It fills the tank in 6 hours, so the rate is 1 tank per 6 hours, which is 1/6 tank per hour.
  • Step 2: Determine the rate at which the emptying pipe works. It empties the tank in 8 hours, so the rate is 1 tank per 8 hours, which is 1/8 tank per hour.
  • Step 3: Calculate the combined rate when both pipes are opened together. Since one pipe fills and the other empties, we subtract the emptying rate from the filling rate: 1/6 - 1/8.
  • Step 4: To subtract the fractions, find a common denominator. The common denominator for 6 and 8 is 24. Convert the rates: 1/6 = 4/24 and 1/8 = 3/24.
  • Step 5: Now subtract the two rates: 4/24 - 3/24 = 1/24 tank per hour.
  • Step 6: To find out how long it takes to fill the tank at the combined rate, take the reciprocal of the combined rate: 1 / (1/24) = 24 hours.
  • Rate of Work – Understanding how to calculate the rates of filling and emptying and how to combine them.
  • Combined Rates – Applying the concept of combined rates to determine the net effect of multiple processes.
  • Time Calculation – Using the formula for time based on the rate of work to find the total time required.
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