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Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both

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Question: Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 7 hours
  2. 8 hours
  3. 9 hours
  4. 10 hours

Correct Answer: 9 hours

Solution: 

The combined rate is 1/12 + 1/18 = 5/36. Therefore, it will take 36/5 = 7.2 hours to fill the tank.

Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both

Practice Questions

Q1
Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
  1. 7 hours
  2. 8 hours
  3. 9 hours
  4. 10 hours

Questions & Step-by-Step Solutions

Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 7.2 hours
  • Step 1: Determine the rate at which pipe A fills the tank. Since it can fill the tank in 12 hours, its rate is 1/12 of the tank per hour.
  • Step 2: Determine the rate at which pipe B fills the tank. Since it can fill the tank in 18 hours, its rate is 1/18 of the tank per hour.
  • Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/12 + 1/18.
  • Step 4: To add 1/12 and 1/18, find a common denominator. The least common multiple of 12 and 18 is 36.
  • Step 5: Convert 1/12 to have a denominator of 36. This becomes 3/36.
  • Step 6: Convert 1/18 to have a denominator of 36. This becomes 2/36.
  • Step 7: Now add the two fractions: 3/36 + 2/36 = 5/36.
  • Step 8: The combined rate of both pipes is 5/36 of the tank per hour.
  • Step 9: To find out how long it takes to fill the tank, take the reciprocal of the combined rate. This means you calculate 1 divided by (5/36).
  • Step 10: The reciprocal of 5/36 is 36/5.
  • Step 11: Calculate 36/5 to find the time in hours. This equals 7.2 hours.
  • Rate of Work – Understanding how to calculate the rate at which multiple entities (pipes) can complete a task (filling a tank) when working together.
  • Fraction Addition – Applying the concept of adding fractions to determine the combined work rate of the two pipes.
  • Time Calculation – Using the combined rate to calculate the total time required to complete the task.
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