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A tank is filled by two pipes in 18 hours and 24 hours respectively. If both pip

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Question: A tank is filled by two pipes in 18 hours and 24 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 8 hours
  2. 10 hours
  3. 12 hours
  4. 14 hours

Correct Answer: 12 hours

Solution: 

The combined rate is 1/18 + 1/24 = 4/72 + 3/72 = 7/72. Therefore, it will take 72/7 hours or approximately 10.29 hours.

A tank is filled by two pipes in 18 hours and 24 hours respectively. If both pip

Practice Questions

Q1
A tank is filled by two pipes in 18 hours and 24 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
  1. 8 hours
  2. 10 hours
  3. 12 hours
  4. 14 hours

Questions & Step-by-Step Solutions

A tank is filled by two pipes in 18 hours and 24 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
  • Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 18 hours, so its rate is 1/18 of the tank per hour.
  • Step 2: The second pipe fills the tank in 24 hours, so its rate is 1/24 of the tank per hour.
  • Step 3: Add the rates of both pipes together to find the combined rate. This is done by finding a common denominator.
  • Step 4: The common denominator for 18 and 24 is 72. Convert the rates: 1/18 = 4/72 and 1/24 = 3/72.
  • Step 5: Add the converted rates: 4/72 + 3/72 = 7/72.
  • Step 6: The combined rate of both pipes is 7/72 of the tank per hour.
  • Step 7: To find out how long it takes to fill the tank, take the reciprocal of the combined rate: 1 / (7/72) = 72/7 hours.
  • Step 8: Calculate 72/7 to find the time in hours, which is approximately 10.29 hours.
  • Work Rate – Understanding how to calculate the combined work rate of two or more entities working together.
  • Fraction Addition – Adding fractions with different denominators to find a common rate.
  • Time Calculation – Calculating the total time taken based on the combined work rate.
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