CAT Exam > CAT Questions > Three pipes P, Q, R can fill a tank in 4, 8 a...
Start Learning for Free
Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?
- a)Q alone is opened
- b)P and S are opened together
- c)P, R and S are opened together
- d)Q, R and S are opened together
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively,...
Suppose the volume of the tank is 120 litres. In 1 hour, P, Q and R can fill 30, 15 and 10 litres respectively while S can empty 12 litres. From this, the effective per hour rates(putting the values in option),
for eg in option pipe
Q = 15,
P and S = 30 - 12 = 18.
P, R, S = 30 + 10 - 12 = 28.
Q, R, S = 15 + 10 - 12 = 13.
Thus for answer choices a to d, the rates are are 15, 18, 28 and 13 litres per hour respectively.Thus if the combination from the option are used to find the time i.e 120/rate, the times taken will be 8, 6.66, 4.28 and 9.23 hours respectively. Hence option C.
Most Upvoted Answer
Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively,...
To find the arrangement that will fill the tank in the least possible time, we need to compare the rates at which each pipe fills or drains the tank. The rate at which a pipe fills or drains the tank can be calculated by taking the reciprocal of the time taken by the pipe to fill or drain the tank.
Let's calculate the rates for each pipe:
- Pipe P can fill the tank in 4 hours, so its filling rate is 1/4 tanks per hour.
- Pipe Q can fill the tank in 8 hours, so its filling rate is 1/8 tanks per hour.
- Pipe R can fill the tank in 12 hours, so its filling rate is 1/12 tanks per hour.
- Pipe S can drain the tank in 10 hours, so its draining rate is -1/10 tanks per hour (negative sign indicates draining).
Now, let's consider each arrangement and calculate the overall rate for each:
a) Q alone is opened:
The overall rate for this arrangement is 1/8 tanks per hour, as Q is the only pipe opened.
b) P and S are opened together:
The overall rate for this arrangement is (1/4 - 1/10) tanks per hour, as P fills the tank and S drains the tank. Simplifying this, we get 3/20 tanks per hour.
c) P, R, and S are opened together:
The overall rate for this arrangement is (1/4 + 1/12 - 1/10) tanks per hour, as P and R fill the tank and S drains the tank. Simplifying this, we get 1/6 tanks per hour.
d) Q, R, and S are opened together:
The overall rate for this arrangement is (1/8 + 1/12 - 1/10) tanks per hour, as Q and R fill the tank and S drains the tank. Simplifying this, we get 7/120 tanks per hour.
From the calculations above, we can see that option c) P, R, and S opened together has the highest overall rate of 1/6 tanks per hour. Therefore, this arrangement will fill the tank in the least possible time.
Let's calculate the rates for each pipe:
- Pipe P can fill the tank in 4 hours, so its filling rate is 1/4 tanks per hour.
- Pipe Q can fill the tank in 8 hours, so its filling rate is 1/8 tanks per hour.
- Pipe R can fill the tank in 12 hours, so its filling rate is 1/12 tanks per hour.
- Pipe S can drain the tank in 10 hours, so its draining rate is -1/10 tanks per hour (negative sign indicates draining).
Now, let's consider each arrangement and calculate the overall rate for each:
a) Q alone is opened:
The overall rate for this arrangement is 1/8 tanks per hour, as Q is the only pipe opened.
b) P and S are opened together:
The overall rate for this arrangement is (1/4 - 1/10) tanks per hour, as P fills the tank and S drains the tank. Simplifying this, we get 3/20 tanks per hour.
c) P, R, and S are opened together:
The overall rate for this arrangement is (1/4 + 1/12 - 1/10) tanks per hour, as P and R fill the tank and S drains the tank. Simplifying this, we get 1/6 tanks per hour.
d) Q, R, and S are opened together:
The overall rate for this arrangement is (1/8 + 1/12 - 1/10) tanks per hour, as Q and R fill the tank and S drains the tank. Simplifying this, we get 7/120 tanks per hour.
From the calculations above, we can see that option c) P, R, and S opened together has the highest overall rate of 1/6 tanks per hour. Therefore, this arrangement will fill the tank in the least possible time.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer?
Question Description
Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer?.
Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Three pipes P, Q, R can fill a tank in 4, 8 and 12 hours respectively, while another pipe S can drain it in 10 hours. Which arrangement will fill the tank in the least possible time?a)Q alone is openedb)P and S are opened togetherc)P, R and S are opened togetherd)Q, R and S are opened togetherCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup