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Two Pipes P and Q can fill a water tank in 15 and 25 minutes respectively and a third pipe R can empty at the rate of 11 gallons per minute. If P, Q, and R are opened together to fill the tank for 30 minutes then find the capacity of the tank.
  • a)
    90
  • b)
    100
  • c)
    180
  • d)
    150
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two Pipes P and Q can fill a water tank in 15 and 25 minutes respectiv...
The key concept to solve this problem is the concept of work done by each pipe in a given time. Let's break down the solution into the following steps:

Step 1: Calculate the work done by each pipe in 1 minute
- Pipe P fills the tank in 15 minutes, so it fills 1/15 of the tank in 1 minute.
- Pipe Q fills the tank in 25 minutes, so it fills 1/25 of the tank in 1 minute.
- Pipe R empties at the rate of 11 gallons per minute, so it empties 11 gallons in 1 minute.

Step 2: Calculate the combined work done by all pipes in 1 minute
- When all three pipes are opened together, the net work done in 1 minute is (1/15 + 1/25 - 11) = (5/75 + 3/75 - 11) = -3/75.
- This means that the combined work done by all pipes together is to empty 3/75th of the tank in 1 minute.

Step 3: Calculate the capacity of the tank
- In 30 minutes, the combined work done by all pipes is to empty (3/75)*30 = 90/75 = 6/5 of the tank.
- Therefore, the capacity of the tank is the reciprocal of 6/5, which is 5/6 of the tank.
- This means the capacity of the tank is 6*5 = 30 gallons.
Therefore, the capacity of the tank is 30 gallons, which corresponds to option 'D'.
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Two Pipes P and Q can fill a water tank in 15 and 25 minutes respectively and a third pipe R can empty at the rate of 11 gallons per minute. If P, Q, and R are opened together to fill the tank for 30 minutes then find the capacity of the tank.a)90b)100c)180d)150Correct answer is option 'D'. Can you explain this answer?
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Two Pipes P and Q can fill a water tank in 15 and 25 minutes respectively and a third pipe R can empty at the rate of 11 gallons per minute. If P, Q, and R are opened together to fill the tank for 30 minutes then find the capacity of the tank.a)90b)100c)180d)150Correct answer is option 'D'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two Pipes P and Q can fill a water tank in 15 and 25 minutes respectively and a third pipe R can empty at the rate of 11 gallons per minute. If P, Q, and R are opened together to fill the tank for 30 minutes then find the capacity of the tank.a)90b)100c)180d)150Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two Pipes P and Q can fill a water tank in 15 and 25 minutes respectively and a third pipe R can empty at the rate of 11 gallons per minute. If P, Q, and R are opened together to fill the tank for 30 minutes then find the capacity of the tank.a)90b)100c)180d)150Correct answer is option 'D'. Can you explain this answer?.
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