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A cistern has two pipes. Pipe A can fill it in 8 hours and pipe B can empty it i

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Question: A cistern has two pipes. Pipe A can fill it in 8 hours and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the cistern?

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 cistern.

A cistern has two pipes. Pipe A can fill it in 8 hours and pipe B can empty it i

Practice Questions

Q1
A cistern has two pipes. Pipe A can fill it in 8 hours and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the cistern?
  1. 4 hours
  2. 6 hours
  3. 8 hours
  4. 10 hours

Questions & Step-by-Step Solutions

A cistern has two pipes. Pipe A can fill it in 8 hours and pipe B can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the cistern?
  • Step 1: Determine the rate at which Pipe A fills the cistern. Since Pipe A can fill the cistern in 8 hours, its rate is 1 cistern per 8 hours, or 1/8 of the cistern per hour.
  • Step 2: Determine the rate at which Pipe B empties the cistern. Since Pipe B can empty the cistern in 12 hours, its rate is 1 cistern per 12 hours, or 1/12 of the cistern per hour.
  • Step 3: Calculate the net rate when both pipes are opened together. The net rate is the filling rate of Pipe A minus the emptying rate of Pipe B: (1/8) - (1/12).
  • Step 4: To subtract the 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).
  • Step 7: The net rate of filling the cistern is 1/24 of the cistern per hour.
  • Step 8: To find out how long it takes to fill the entire cistern, 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 pipes fill or empty a cistern.
  • Net Rate Calculation – Combining the rates of filling and emptying to find the effective rate.
  • Time Calculation – Using the net rate to determine the total time required to fill the cistern.
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