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A tank is filled by two pipes in 15 and 20 minutes respectively. If both pipes a

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Question: A tank is filled by two pipes in 15 and 20 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 8 minutes
  2. 10 minutes
  3. 12 minutes
  4. 15 minutes

Correct Answer: 10 minutes

Solution: 

The combined rate is 1/15 + 1/20 = 7/60. Therefore, time taken = 60/7 ≈ 8.57 minutes.

A tank is filled by two pipes in 15 and 20 minutes respectively. If both pipes a

Practice Questions

Q1
A tank is filled by two pipes in 15 and 20 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?
  1. 8 minutes
  2. 10 minutes
  3. 12 minutes
  4. 15 minutes

Questions & Step-by-Step Solutions

A tank is filled by two pipes in 15 and 20 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 8.57 minutes
  • Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 15 minutes, so its rate is 1/15 of the tank per minute.
  • Step 2: The second pipe fills the tank in 20 minutes, so its rate is 1/20 of the tank per minute.
  • Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/15 + 1/20.
  • Step 4: To add the fractions, find a common denominator. The least common multiple of 15 and 20 is 60.
  • Step 5: Convert the fractions: 1/15 becomes 4/60 and 1/20 becomes 3/60.
  • Step 6: Now add the two fractions: 4/60 + 3/60 = 7/60.
  • Step 7: The combined rate of both pipes is 7/60 of the tank per minute.
  • Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 / (7/60) = 60/7 minutes.
  • Step 9: Calculate 60/7, which is approximately 8.57 minutes.
  • Rate of Work – Understanding how to calculate the combined work rate of multiple entities working together.
  • Time Calculation – Applying the formula for time based on the combined rate of work to find the total time taken.
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