DIRECTIONS for questions: Select the correct alternative from the given choices.There are five pipes P1, P2, P3, P4 and P5 which can fill a tank in 45, 30, 15, 10 and 9 minutes respectively. Exactly two of the pipes are now converted into emptying pipes retaining the same respective flow rates. If one filling pipe and one emptying pipe operate, the empty tank gets filled in 12 x 6 / 7 minutes, while for another combination of a filling pipe and an emptying pipe, the full tank gets emptied in 22 x 1 / 2 minutes. Which of the following pipes may have been converted into emptying pipes?a)P1, P2b)P2, P3c)P3, P4d)P4, P5Correct answer is option 'C'. Can you explain this answer?

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DIRECTIONS for questions: Select the correct alternative from the given choices.

There are five pipes P₁, P₂, P₃, P₄ and P₅which can fill a tank in 45, 30, 15, 10 and 9 minutes respectively. Exactly two of the pipes are now converted into emptying pipes retaining the same respective flow rates. If one filling pipe and one emptying pipe operate, the empty tank gets filled in 12 x 6 / 7 minutes, while for another combination of a filling pipe and an emptying pipe, the full tank gets emptied in 22 x 1 / 2 minutes. Which of the following pipes may have been converted into emptying pipes?

a)
P₁, P₂
b)
P₂, P₃
c)
P₃, P₄
d)
P₄, P₅

Correct answer is option 'C'. Can you explain this answer?

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DIRECTIONS for questions: Select the correct alternative from the give...

Considering 90 as the capacity of the tank {LCM of (45, 30, 15, 10, 9) we can find therate of flow for the 5 pipes as 90 / 45,90 / 30, 90 / 15, 90 / 10 and 90 / 9 respectively. The time and the rates of the 5 pipes are tabulated below.

If the tank gets filled in 12 x 6 / 7 min, effective rate of filing

= 90 / (90 / 7)= 7 units/min

If the tank gets emptied in 22 x 1 / 2min, effective rate of emptying = 90 / (45 / 2)= 4 units/min

7 units/min can be obtained by making P₄ a filling pipe and P₁ emptying pipe or Pe filling and P₂ emptying. If P₄ is filling pipe and P₁ emptying pipe, 4 units/min can be obtained by making P₅ emptying pipe and P₃ filling pipe. In the latter case, P₃ emptying and P₁ filling pipe.

Case(i):7 = 10-3 = P₅-P₂

-4 = 2 - 6 = P₁ - P₃

Case(ii):7 = 9- 2 = P₄ – P₁

-4 = 6- 10 = P₃-P₅

∴P₁, P₅ or P₃, P₂ may have been converted to emptying pipes. Only P2, P3 is listed among the options.

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DIRECTIONS for questions: Select the correct alternative from the give...

Given:
- Pipes P1, P2, P3, P4, and P5 can fill a tank in 45, 30, 15, 10, and 9 minutes respectively.
- Two of the pipes have been converted into emptying pipes while retaining the same respective flow rates.
- One filling pipe and one emptying pipe operating together can fill the empty tank in 12 x 6 / 7 minutes.
- Another combination of a filling pipe and an emptying pipe can empty the full tank in 22 x 1 / 2 minutes.

To find:
Which pipes may have been converted into emptying pipes.

Solution:
Let's assume the flow rates of the filling pipes and emptying pipes are denoted as F1, F2, F3, F4, and F5.

Flow rates for filling pipes:
F1 = 1/45 (as P1 can fill the tank in 45 minutes)
F2 = 1/30 (as P2 can fill the tank in 30 minutes)
F3 = 1/15 (as P3 can fill the tank in 15 minutes)
F4 = 1/10 (as P4 can fill the tank in 10 minutes)
F5 = 1/9 (as P5 can fill the tank in 9 minutes)

Now, let's consider the first combination where one filling pipe and one emptying pipe operate to fill the empty tank in 12 x 6 / 7 minutes.

- The filling pipe's flow rate is Fx (unknown)
- The emptying pipe's flow rate is Fy (unknown)

The equation for this combination can be written as:
1/Fx - 1/Fy = 7/72 (as the tank gets filled in 12 x 6 / 7 minutes)

Similarly, let's consider the second combination where one filling pipe and one emptying pipe operate to empty the full tank in 22 x 1 / 2 minutes.

- The filling pipe's flow rate is Fm (unknown)
- The emptying pipe's flow rate is Fn (unknown)

The equation for this combination can be written as:
1/Fm + 1/Fn = 2/22 (as the full tank gets emptied in 22 x 1 / 2 minutes)

Now, we need to check which combination of emptying pipes satisfies both equations simultaneously.

Let's substitute the flow rates of the pipes and solve the equations:

For the first combination:
1/Fx - 1/Fy = 7/72

Substituting the flow rates:
1/Fx - 1/Fy = 7/72
1/Fx - 1/Fy = 1/10 - 1/9
1/Fx - 1/Fy = (9 - 10)/90
1/Fx - 1/Fy = -1/90

For the second combination:
1/Fm + 1/Fn = 2/22

Substituting the flow rates:
1/Fm + 1/Fn = 2/22
1/Fm + 1/Fn = 1/11 - 1/9
1/Fm + 1/Fn = (9 - 11)/99
1/Fm + 1/Fn = -2/99

By comparing the two equations, we can see that the flow rates of

Answered by Wizius Careers · View profile

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DIRECTIONS for questions: Select the correct alternative from the given choices.There are five pipes P1, P2, P3, P4 and P5 which can fill a tank in 45, 30, 15, 10 and 9 minutes respectively. Exactly two of the pipes are now converted into emptying pipes retaining the same respective flow rates. If one filling pipe and one emptying pipe operate, the empty tank gets filled in 12 x 6 / 7 minutes, while for another combination of a filling pipe and an emptying pipe, the full tank gets emptied in 22 x 1 / 2 minutes. Which of the following pipes may have been converted into emptying pipes?a)P1, P2b)P2, P3c)P3, P4d)P4, P5Correct answer is option 'C'. Can you explain this answer?

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DIRECTIONS for questions: Select the correct alternative from the given choices.There are five pipes P1, P2, P3, P4 and P5 which can fill a tank in 45, 30, 15, 10 and 9 minutes respectively. Exactly two of the pipes are now converted into emptying pipes retaining the same respective flow rates. If one filling pipe and one emptying pipe operate, the empty tank gets filled in 12 x 6 / 7 minutes, while for another combination of a filling pipe and an emptying pipe, the full tank gets emptied in 22 x 1 / 2 minutes. Which of the following pipes may have been converted into emptying pipes?a)P1, P2b)P2, P3c)P3, P4d)P4, P5Correct answer is option 'C'. 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 questions: Select the correct alternative from the given choices.There are five pipes P1, P2, P3, P4 and P5 which can fill a tank in 45, 30, 15, 10 and 9 minutes respectively. Exactly two of the pipes are now converted into emptying pipes retaining the same respective flow rates. If one filling pipe and one emptying pipe operate, the empty tank gets filled in 12 x 6 / 7 minutes, while for another combination of a filling pipe and an emptying pipe, the full tank gets emptied in 22 x 1 / 2 minutes. Which of the following pipes may have been converted into emptying pipes?a)P1, P2b)P2, P3c)P3, P4d)P4, P5Correct answer is option 'C'. 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 questions: Select the correct alternative from the given choices.There are five pipes P1, P2, P3, P4 and P5 which can fill a tank in 45, 30, 15, 10 and 9 minutes respectively. Exactly two of the pipes are now converted into emptying pipes retaining the same respective flow rates. If one filling pipe and one emptying pipe operate, the empty tank gets filled in 12 x 6 / 7 minutes, while for another combination of a filling pipe and an emptying pipe, the full tank gets emptied in 22 x 1 / 2 minutes. Which of the following pipes may have been converted into emptying pipes?a)P1, P2b)P2, P3c)P3, P4d)P4, P5Correct answer is option 'C'. Can you explain this answer?.

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