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A tank is filled by two pipes in 9 hours and 12 hours respectively. If the first

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Question: A tank is filled by two pipes in 9 hours and 12 hours respectively. If the first pipe is opened for 3 hours and then the second pipe is opened, how long will it take to fill the tank?

Options:

  1. 5 hours
  2. 6 hours
  3. 7 hours
  4. 8 hours

Correct Answer: 6 hours

Solution: 

In 3 hours, the first pipe fills 3/9 = 1/3 of the tank. The remaining 2/3 can be filled by both pipes in 2 hours.

A tank is filled by two pipes in 9 hours and 12 hours respectively. If the first

Practice Questions

Q1
A tank is filled by two pipes in 9 hours and 12 hours respectively. If the first pipe is opened for 3 hours and then the second pipe is opened, how long will it take to fill the tank?
  1. 5 hours
  2. 6 hours
  3. 7 hours
  4. 8 hours

Questions & Step-by-Step Solutions

A tank is filled by two pipes in 9 hours and 12 hours respectively. If the first pipe is opened for 3 hours and then the second pipe is opened, 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 9 hours, so its rate is 1/9 of the tank per hour. The second pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour.
  • Step 2: Calculate how much of the tank the first pipe fills in 3 hours. Since it fills 1/9 of the tank in 1 hour, in 3 hours it fills 3/9, which simplifies to 1/3 of the tank.
  • Step 3: Determine how much of the tank is left to fill after the first pipe has been running for 3 hours. Since 1/3 of the tank is filled, the remaining part is 1 - 1/3 = 2/3 of the tank.
  • Step 4: Now, both pipes are opened to fill the remaining 2/3 of the tank. The combined rate of both pipes is (1/9 + 1/12) of the tank per hour.
  • Step 5: Find a common denominator to add the rates. The least common multiple of 9 and 12 is 36. Convert the rates: 1/9 = 4/36 and 1/12 = 3/36. So, the combined rate is 4/36 + 3/36 = 7/36 of the tank per hour.
  • Step 6: To find out how long it takes to fill the remaining 2/3 of the tank at the combined rate of 7/36, set up the equation: (7/36) * time = 2/3.
  • Step 7: Solve for time. Multiply both sides by 36 to eliminate the fraction: 7 * time = 2/3 * 36. This simplifies to 7 * time = 24.
  • Step 8: Divide both sides by 7 to find time: time = 24/7 hours, which is approximately 3.43 hours.
  • Rate of Work – Understanding how to calculate the rate at which each pipe fills the tank and how to combine their rates.
  • Time Management – Determining the total time taken to fill the tank by considering the sequential operation of the pipes.
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