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A tank is filled by two pipes in 12 hours and 15 hours respectively. If the firs

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Question: A tank is filled by two pipes in 12 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank completely?

Options:

  1. 6 hours
  2. 7 hours
  3. 8 hours
  4. 9 hours

Correct Answer: 8 hours

Solution: 

In 5 hours, the first pipe fills 5/12 of the tank. The remaining is 1 - 5/12 = 7/12. The combined rate of both pipes is 1/12 + 1/15 = 7/60. Therefore, it will take (7/12) / (7/60) = 60/12 = 5 hours to fill the remaining part.

A tank is filled by two pipes in 12 hours and 15 hours respectively. If the firs

Practice Questions

Q1
A tank is filled by two pipes in 12 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank completely?
  1. 6 hours
  2. 7 hours
  3. 8 hours
  4. 9 hours

Questions & Step-by-Step Solutions

A tank is filled by two pipes in 12 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank completely?
Correct Answer: 10 hours
  • Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour. The second pipe fills the tank in 15 hours, so its rate is 1/15 of the tank per hour.
  • Step 2: Calculate how much of the tank the first pipe fills in 5 hours. Since the first pipe fills 1/12 of the tank in 1 hour, in 5 hours it fills 5/12 of the tank.
  • Step 3: Find out how much of the tank is left to fill after the first pipe has been running for 5 hours. The remaining part of the tank is 1 - 5/12 = 7/12.
  • Step 4: Calculate the combined rate of both pipes when they are both open. The combined rate is 1/12 + 1/15. To add these fractions, find a common denominator, which is 60. So, (5/60) + (4/60) = 9/60 = 3/20.
  • Step 5: Determine how long it will take to fill the remaining 7/12 of the tank with both pipes open. Use the formula: time = remaining part / combined rate. This gives us (7/12) / (3/20).
  • Step 6: Simplify the calculation: (7/12) * (20/3) = (7 * 20) / (12 * 3) = 140 / 36 = 35/9 hours.
  • Step 7: Convert 35/9 hours into hours and minutes. 35/9 hours is approximately 3.89 hours, which is 3 hours and 53 minutes.
  • Rate of Work – Understanding how to calculate the rate at which each pipe fills the tank and how to combine their rates.
  • Fraction of Work Done – Calculating the fraction of the tank filled by the first pipe before the second pipe is opened.
  • Time Calculation – Determining the time required to fill the remaining part of the tank after the first pipe has been used.
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