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A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time that C, the 3rd pipe, alone takes to empty it. Pipe A, working alone, takes half the time taken by the pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours, is
  • a)
    15
  • b)
    10
  • c)
    30
  • d)
    7
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A swimming pool has 3 drain pipes. The first two pipes A and B, operat...
Given:
- Pipe A and B together can empty the pool in half the time taken by pipe C alone.
- Pipe A takes half the time taken by pipe B.
- Together, pipe A and B take 6 hours 40 minutes to empty the pool.

To find:
The time taken by pipe A to empty the pool.

Solution:

Let's assume that pipe C takes x hours to empty the pool.

The rate of work of pipe C is 1/x of the pool per hour.

Rate of work of pipe A:
Since pipe A takes half the time taken by pipe B, let's assume that pipe B takes y hours to empty the pool. So, pipe A takes y/2 hours to empty the pool.
Therefore, the rate of work of pipe A is 1/(y/2) = 2/y of the pool per hour.

Rate of work of pipe B:
The combined rate of work of pipe A and B is 1/(6 hours 40 minutes) = 1/(6 + 40/60) = 1/(6 + 2/3) = 1/(18/3 + 2/3) = 1/(20/3) = 3/20 of the pool per hour.
Since pipe A's rate of work is 2/y of the pool per hour, the rate of work of pipe B is (3/20) - (2/y) = (3y - 40)/(20y) of the pool per hour.

Rate of work of pipe C:
Since pipe B and C together can empty the pool in half the time taken by pipe C alone, their combined rate of work is 2 times the rate of work of pipe C.
So, (3y - 40)/(20y) + 1/x = 2 * (1/x)

Simplifying the equation:
(3y - 40)/(20y) + 1/x = 2/x
(3y - 40)/(20y) = 1/x
x/(3y - 40) = 20y

Cross multiplying:
20xy = 3xy - 40x
17xy = 40x

Simplifying further:
17y = 40

Therefore, y = 40/17

Time taken by pipe A:
Pipe A takes half the time taken by pipe B, so the time taken by pipe A is (40/17)/2 = 20/17 hours.

Converting the time to minutes:
20/17 * 60 = 1200/17 minutes

Converting the minutes to hours and minutes:
1200/17 minutes = 70 minutes + (20/17) * 60 minutes
= 70 minutes + 1200/17 minutes
= 70 minutes + 70.59 minutes
≈ 140.59 minutes

Converting the minutes to hours:
140.59 minutes ÷ 60 = 2.34 hours

So, the time taken by pipe A to empty the pool is approximately 2.34 hours, which is closest to option A) 15 hours.
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Community Answer
A swimming pool has 3 drain pipes. The first two pipes A and B, operat...
Time taken by Pipe B is 2x hours.
Time taken by Pipe A is x hours
Time taken by Pipe C 
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A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time that C, the 3rd pipe, alone takes to empty it. Pipe A, working alone, takes half the time taken by the pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours, isa)15b)10c)30d)7e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time that C, the 3rd pipe, alone takes to empty it. Pipe A, working alone, takes half the time taken by the pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours, isa)15b)10c)30d)7e)None of theseCorrect answer is option 'A'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time that C, the 3rd pipe, alone takes to empty it. Pipe A, working alone, takes half the time taken by the pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours, isa)15b)10c)30d)7e)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time that C, the 3rd pipe, alone takes to empty it. Pipe A, working alone, takes half the time taken by the pipe B. Together they take 6 hours 40 minutes to empty the pool. Time taken by pipe A to empty the pool, in hours, isa)15b)10c)30d)7e)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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