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A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?
- a)30 mins
- b)25 mins
- c)45 mins
- d)50 mins
- e)None of the Above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A pipe can fill a tank in 12 minutes and another pipe can fill it in 1...
x/6 – (x+5)/12 – (x+5)/15 = 0
x = 45 mins
x = 45 mins
Most Upvoted Answer
A pipe can fill a tank in 12 minutes and another pipe can fill it in 1...
x/6 – (x+5)/12 – (x+5)/15 = 0
x = 45 mins
x = 45 mins
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Community Answer
A pipe can fill a tank in 12 minutes and another pipe can fill it in 1...
Given:
Pipe 1 can fill the tank in 12 minutes.
Pipe 2 can fill the tank in 15 minutes.
Pipe 3 can empty the tank in 6 minutes.
Approach:
We need to find the time taken to empty the water tank. We can solve this problem by using the concept of work.
1. Calculate the work done by each pipe per minute:
- Pipe 1: 1/12 (since it takes 12 minutes to fill the tank)
- Pipe 2: 1/15 (since it takes 15 minutes to fill the tank)
- Pipe 3: -1/6 (since it empties the tank)
2. Calculate the work done by the first two pipes in 5 minutes:
- Pipe 1: (1/12) * 5 = 5/12
- Pipe 2: (1/15) * 5 = 5/15 = 1/3
3. Calculate the net work done by all three pipes in 5 minutes:
Net work done = (work done by pipe 1 + work done by pipe 2 + work done by pipe 3)
= (5/12 + 1/3 - 1/6)
= (10/24 + 8/24 - 4/24)
= 14/24
= 7/12
4. Calculate the remaining work to be done:
Remaining work = 1 - (net work done in 5 minutes)
= 1 - (7/12)
= 5/12
5. Calculate the time taken to empty the tank using pipe 3:
(work done by pipe 3) * (time taken) = remaining work
(-1/6) * (time taken) = 5/12
time taken = (5/12) / (-1/6)
= (5/12) * (-6/1)
= -30/12
= -2.5
Since time cannot be negative, we take the absolute value of -2.5, which gives us the time taken to empty the tank as 2.5 minutes.
Therefore, the correct answer is option C) 45 minutes.
Pipe 1 can fill the tank in 12 minutes.
Pipe 2 can fill the tank in 15 minutes.
Pipe 3 can empty the tank in 6 minutes.
Approach:
We need to find the time taken to empty the water tank. We can solve this problem by using the concept of work.
1. Calculate the work done by each pipe per minute:
- Pipe 1: 1/12 (since it takes 12 minutes to fill the tank)
- Pipe 2: 1/15 (since it takes 15 minutes to fill the tank)
- Pipe 3: -1/6 (since it empties the tank)
2. Calculate the work done by the first two pipes in 5 minutes:
- Pipe 1: (1/12) * 5 = 5/12
- Pipe 2: (1/15) * 5 = 5/15 = 1/3
3. Calculate the net work done by all three pipes in 5 minutes:
Net work done = (work done by pipe 1 + work done by pipe 2 + work done by pipe 3)
= (5/12 + 1/3 - 1/6)
= (10/24 + 8/24 - 4/24)
= 14/24
= 7/12
4. Calculate the remaining work to be done:
Remaining work = 1 - (net work done in 5 minutes)
= 1 - (7/12)
= 5/12
5. Calculate the time taken to empty the tank using pipe 3:
(work done by pipe 3) * (time taken) = remaining work
(-1/6) * (time taken) = 5/12
time taken = (5/12) / (-1/6)
= (5/12) * (-6/1)
= -30/12
= -2.5
Since time cannot be negative, we take the absolute value of -2.5, which gives us the time taken to empty the tank as 2.5 minutes.
Therefore, the correct answer is option C) 45 minutes.
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A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?a)30 minsb)25 minsc)45 minsd)50 minse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?a)30 minsb)25 minsc)45 minsd)50 minse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?a)30 minsb)25 minsc)45 minsd)50 minse)None of the AboveCorrect answer is option 'C'. Can you explain this answer?.
A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?a)30 minsb)25 minsc)45 minsd)50 minse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?a)30 minsb)25 minsc)45 minsd)50 minse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?a)30 minsb)25 minsc)45 minsd)50 minse)None of the AboveCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?a)30 minsb)25 minsc)45 minsd)50 minse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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