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Directions for Question : A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.
Q. If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?
- a)16 minutes
- b)13 minutes
- c)7 minutes
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Directions for Question :A set of 10 pipes (set X) can fill 70% of a t...
►Set X will do 5% per minute and Set Y will do 6.25% per minute, while set Z will do 5% per minute (negative work).
►Hence, Net work will be 6.25% per minute. To fill 49% it will take slightly less than eight minutes and the value will be a fraction.
►None of the first three options matches this requirement.
Most Upvoted Answer
Directions for Question :A set of 10 pipes (set X) can fill 70% of a t...
Solution:
Given,
Set X (10 pipes) can fill 70% of a tank in 7 minutes
Set Y (5 pipes) fills 3/8 of the tank in 3 minutes
Set Z (8 pipes) can empty 5/10 of the tank in 10 minutes
Let the capacity of the tank be C.
Set X can fill 70% of the tank in 7 minutes.
Hence, to fill 100% of the tank, time taken by set X = (7 × 100)/70 = 10 minutes.
Set Y fills 3/8 of the tank in 3 minutes.
Hence, to fill 100% of the tank, time taken by set Y = (3 × 8)/3 = 8 minutes.
Set Z can empty 5/10 of the tank in 10 minutes.
Hence, to empty 100% of the tank, time taken by set Z = (10 × 10)/(5/10) = 200 minutes.
Let the number of pipes in set X that are closed be 5.
Then, the number of pipes in set X that are open = 10 - 5 = 5.
Let the number of pipes in set Y that are open be 2.5.
Then, the number of pipes in set Y that are closed = 5 - 2.5 = 2.5.
Let the time taken to fill 49% of the tank be t minutes.
We can find the rate of each set of pipes using the formula, rate = work/time.
Rate of set X = 70/7 = 10% per minute.
Rate of set Y = (3/8)/3 = 1/8 = 12.5% per minute.
Rate of set Z = -50/(5/10 × 10) = -100% per minute (negative sign indicates that it is emptying the tank).
Let the total rate of all the pipes that are open be R.
Then, R = 5 × 10% + 2.5 × 12.5% + 8 × (-100%) = -70%.
Hence, the remaining 49% of the tank will be filled at a rate of 70% - 49% = 21% per minute.
Thus, the equation can be written as:
5 × 10% × (t/2) + 2.5 × 12.5% × t/2 - 8 × 100% × t/2 + 21% × t/2 = 49%
Simplifying the above equation, we get:
t = 56 minutes.
Therefore, the correct answer is option D.
Given,
Set X (10 pipes) can fill 70% of a tank in 7 minutes
Set Y (5 pipes) fills 3/8 of the tank in 3 minutes
Set Z (8 pipes) can empty 5/10 of the tank in 10 minutes
Let the capacity of the tank be C.
Set X can fill 70% of the tank in 7 minutes.
Hence, to fill 100% of the tank, time taken by set X = (7 × 100)/70 = 10 minutes.
Set Y fills 3/8 of the tank in 3 minutes.
Hence, to fill 100% of the tank, time taken by set Y = (3 × 8)/3 = 8 minutes.
Set Z can empty 5/10 of the tank in 10 minutes.
Hence, to empty 100% of the tank, time taken by set Z = (10 × 10)/(5/10) = 200 minutes.
Let the number of pipes in set X that are closed be 5.
Then, the number of pipes in set X that are open = 10 - 5 = 5.
Let the number of pipes in set Y that are open be 2.5.
Then, the number of pipes in set Y that are closed = 5 - 2.5 = 2.5.
Let the time taken to fill 49% of the tank be t minutes.
We can find the rate of each set of pipes using the formula, rate = work/time.
Rate of set X = 70/7 = 10% per minute.
Rate of set Y = (3/8)/3 = 1/8 = 12.5% per minute.
Rate of set Z = -50/(5/10 × 10) = -100% per minute (negative sign indicates that it is emptying the tank).
Let the total rate of all the pipes that are open be R.
Then, R = 5 × 10% + 2.5 × 12.5% + 8 × (-100%) = -70%.
Hence, the remaining 49% of the tank will be filled at a rate of 70% - 49% = 21% per minute.
Thus, the equation can be written as:
5 × 10% × (t/2) + 2.5 × 12.5% × t/2 - 8 × 100% × t/2 + 21% × t/2 = 49%
Simplifying the above equation, we get:
t = 56 minutes.
Therefore, the correct answer is option D.
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Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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ample number of questions to practice Directions for Question :A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.Q.If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?a)16 minutesb)13 minutesc)7 minutesd)None of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
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