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Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?
- a)2 hours
- b)3 hours
- c)4 hours
- d)5 hours
- e)None of the Above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P ...
In 1 hour, P can fill = 1/2 Part
Time taken to fill the Cistern by Pipe P = 2 hours
In 1 hour, Q can fill = 1/3 Part
Time taken to fill the Cistern by Pipe P = 3 hours
[1/2 + 1/3 – 1/R] = 7/12
1/R = 1/4
Time required to empty the Cistern = 4 hours
Time taken to fill the Cistern by Pipe P = 2 hours
In 1 hour, Q can fill = 1/3 Part
Time taken to fill the Cistern by Pipe P = 3 hours
[1/2 + 1/3 – 1/R] = 7/12
1/R = 1/4
Time required to empty the Cistern = 4 hours
Most Upvoted Answer
Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P ...
In 1 hour, P can fill = 1/2 Part
Time taken to fill the Cistern by Pipe P = 2 hours
In 1 hour, Q can fill = 1/3 Part
Time taken to fill the Cistern by Pipe P = 3 hours
[1/2 + 1/3 – 1/R] = 7/12
1/R = 1/4
Time required to empty the Cistern = 4 hours
Time taken to fill the Cistern by Pipe P = 2 hours
In 1 hour, Q can fill = 1/3 Part
Time taken to fill the Cistern by Pipe P = 3 hours
[1/2 + 1/3 – 1/R] = 7/12
1/R = 1/4
Time required to empty the Cistern = 4 hours
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Community Answer
Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P ...
To solve this problem, we can find the rates at which each pipe fills or empties the cistern, and then use these rates to determine the time required to empty the cistern completely.
Given information:
- Pipe P can fill 1/2 of the cistern in one hour.
- Pipe Q can fill 1/3 of the cistern in one hour.
- Pipe R is connected to empty the cistern.
Let's calculate the rates at which each pipe fills or empties the cistern:
- Pipe P fills 1/2 of the cistern in one hour, so its filling rate is 1/2 per hour.
- Pipe Q fills 1/3 of the cistern in one hour, so its filling rate is 1/3 per hour.
- Pipe R empties the cistern, so its emptying rate is -1 per hour.
Next, let's determine the combined rate at which all three pipes are filling or emptying the cistern:
- The combined rate is the sum of the individual rates of the pipes.
- Pipe P and Q are filling the cistern, so their rates are added.
- Pipe R is emptying the cistern, so its rate is subtracted.
- The combined rate is (1/2 + 1/3) - 1 = 5/6 - 1 = -1/6 per hour.
Now, let's calculate the time required to empty 7/12 of the cistern:
- The fraction of the cistern emptied is 7/12.
- The combined rate at which the cistern is being emptied is -1/6 per hour.
- We can set up a proportion to find the time required: (7/12) / 1 = x / (-1/6).
- Solving for x, we find x = (-1/6) * (12/7) = -2/7.
- The negative sign indicates that the cistern is being emptied, so we take the absolute value of x, which is 2/7.
Therefore, the time required to empty the cistern completely is 2/7 hours, which is approximately 0.286 hours or 17 minutes.
So the correct answer is option C) 4 hours.
Given information:
- Pipe P can fill 1/2 of the cistern in one hour.
- Pipe Q can fill 1/3 of the cistern in one hour.
- Pipe R is connected to empty the cistern.
Let's calculate the rates at which each pipe fills or empties the cistern:
- Pipe P fills 1/2 of the cistern in one hour, so its filling rate is 1/2 per hour.
- Pipe Q fills 1/3 of the cistern in one hour, so its filling rate is 1/3 per hour.
- Pipe R empties the cistern, so its emptying rate is -1 per hour.
Next, let's determine the combined rate at which all three pipes are filling or emptying the cistern:
- The combined rate is the sum of the individual rates of the pipes.
- Pipe P and Q are filling the cistern, so their rates are added.
- Pipe R is emptying the cistern, so its rate is subtracted.
- The combined rate is (1/2 + 1/3) - 1 = 5/6 - 1 = -1/6 per hour.
Now, let's calculate the time required to empty 7/12 of the cistern:
- The fraction of the cistern emptied is 7/12.
- The combined rate at which the cistern is being emptied is -1/6 per hour.
- We can set up a proportion to find the time required: (7/12) / 1 = x / (-1/6).
- Solving for x, we find x = (-1/6) * (12/7) = -2/7.
- The negative sign indicates that the cistern is being emptied, so we take the absolute value of x, which is 2/7.
Therefore, the time required to empty the cistern completely is 2/7 hours, which is approximately 0.286 hours or 17 minutes.
So the correct answer is option C) 4 hours.
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Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?a)2 hoursb)3 hoursc)4 hoursd)5 hourse)None of the AboveCorrect answer is option 'C'. Can you explain this answer?
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Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?a)2 hoursb)3 hoursc)4 hoursd)5 hourse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?a)2 hoursb)3 hoursc)4 hoursd)5 hourse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?a)2 hoursb)3 hoursc)4 hoursd)5 hourse)None of the AboveCorrect answer is option 'C'. Can you explain this answer?.
Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?a)2 hoursb)3 hoursc)4 hoursd)5 hourse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?a)2 hoursb)3 hoursc)4 hoursd)5 hourse)None of the AboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?a)2 hoursb)3 hoursc)4 hoursd)5 hourse)None of the AboveCorrect answer is option 'C'. Can you explain this answer?.
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