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If a cistern is filled by two pipes in 12 hours and 15 hours respectively, how l

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Question: If a cistern is filled by two pipes in 12 hours and 15 hours respectively, how long will it take to fill the cistern if both pipes are opened together?

Options:

  1. 6 hours
  2. 7.2 hours
  3. 8 hours
  4. 9 hours

Correct Answer: 7.2 hours

Solution: 

The combined rate is 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20. Therefore, it will take 20/3 hours or 6.67 hours.

If a cistern is filled by two pipes in 12 hours and 15 hours respectively, how l

Practice Questions

Q1
If a cistern is filled by two pipes in 12 hours and 15 hours respectively, how long will it take to fill the cistern if both pipes are opened together?
  1. 6 hours
  2. 7.2 hours
  3. 8 hours
  4. 9 hours

Questions & Step-by-Step Solutions

If a cistern is filled by two pipes in 12 hours and 15 hours respectively, how long will it take to fill the cistern if both pipes are opened together?
  • Step 1: Understand that each pipe fills the cistern at a different rate. The first pipe fills it in 12 hours, and the second pipe fills it in 15 hours.
  • Step 2: Calculate the rate of the first pipe. If it fills the cistern in 12 hours, its rate is 1/12 of the cistern per hour.
  • Step 3: Calculate the rate of the second pipe. If it fills the cistern in 15 hours, its rate is 1/15 of the cistern per hour.
  • Step 4: Add the rates of both pipes together to find the combined rate. This is done by adding 1/12 and 1/15.
  • Step 5: To add 1/12 and 1/15, find a common denominator. The least common multiple of 12 and 15 is 60.
  • Step 6: Convert 1/12 to 5/60 (because 1/12 = 5/60) and convert 1/15 to 4/60 (because 1/15 = 4/60).
  • Step 7: Now add the two fractions: 5/60 + 4/60 = 9/60.
  • Step 8: Simplify 9/60 to 3/20. This means together, both pipes fill 3/20 of the cistern in one hour.
  • Step 9: To find out how long it takes to fill the entire cistern, take the reciprocal of the combined rate: 20/3 hours.
  • Step 10: Convert 20/3 hours into a more understandable format. 20/3 hours is approximately 6.67 hours.
  • Work Rate – Understanding how to calculate the combined work rate of multiple entities working together.
  • Fraction Addition – Adding fractions with different denominators to find a common rate.
  • Time Calculation – Converting the combined work rate into time taken to complete the task.
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