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A tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If

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Question: A tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If pipe A is opened for 4 hours and then pipe B is opened, how long will it take to fill the tank?

Options:

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

Correct Answer: 10 hours

Solution: 

In 4 hours, A fills 1/3 of the tank. The remaining 2/3 can be filled by A and B together in 4 hours.

A tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If

Practice Questions

Q1
A tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If pipe A is opened for 4 hours and then pipe B is opened, 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 A and B in 12 hours and 16 hours respectively. If pipe A is opened for 4 hours and then pipe B is opened, how long will it take to fill the tank?
Correct Answer: 8 hours
  • Step 1: Determine the rate at which pipe A fills the tank. Since pipe A fills 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 pipe B fills the tank in 16 hours, its rate is 1/16 of the tank per hour.
  • Step 3: Calculate how much of the tank pipe A fills in 4 hours. In 4 hours, pipe A fills 4 * (1/12) = 4/12 = 1/3 of the tank.
  • Step 4: Determine how much of the tank is left to fill after 4 hours. Since 1/3 of the tank is filled, the remaining part is 1 - 1/3 = 2/3 of the tank.
  • Step 5: Calculate the combined rate of pipes A and B when both are opened. The combined rate is (1/12 + 1/16). To add these, find a common denominator, which is 48. So, (4/48 + 3/48) = 7/48 of the tank per hour.
  • Step 6: Determine how long it takes for pipes A and B together to fill the remaining 2/3 of the tank. Set up the equation: (7/48) * time = 2/3. Solving for time gives time = (2/3) / (7/48) = (2/3) * (48/7) = 16/7 hours.
  • Step 7: Convert 16/7 hours into hours and minutes. 16/7 hours is approximately 2 hours and 18 minutes.
  • 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 how to effectively manage the time each pipe is open to maximize efficiency in filling the tank.
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