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There are three taps P, Q and R. P takes thrice as much time as Q and R together to fill a tank. Q takes twice as much time as P and R together to fill the tank. In how much time (in hours) can R fill the tank individually, if the three together require 10 hours to fill the tank when opened simultaneously?
Most Upvoted Answer
There are three taps P, Q and R. P takes thrice as much time as Q and ...
Given Information:
- P takes thrice as much time as Q and R together to fill the tank
- Q takes twice as much time as P and R together to fill the tank
- Together, P, Q, and R can fill the tank in 10 hours

Let's assume:
- Let the time taken by P to fill the tank be x hours
- Let the time taken by Q to fill the tank be y hours
- Let the time taken by R to fill the tank be z hours

Calculating the relationship between P, Q, and R:
- From the given information, we can write the following equations:
1. x = 3(y + z) (P takes thrice as much time as Q and R together)
2. y = 2(x + z) (Q takes twice as much time as P and R together)
3. 1/x + 1/y + 1/z = 1/10 (Together, P, Q, and R can fill the tank in 10 hours)

Solving the equations:
- Substitute the values of x and y from equations 1 and 2 into equation 3:
1/(3y + 3z) + 1/(2x + 2z) + 1/z = 1/10
1/(3y + 3z) + 1/(2(3y + 3z) + 2z) + 1/z = 1/10
1/(3y + 3z) + 1/(6y + 6z + 2z) + 1/z = 1/10
1/(3y + 3z) + 1/(6y + 8z) + 1/z = 1/10
(6y + 8z + 3y + 3z + 3z) / [(3y + 3z)(6y + 8z)] = 1/10
(9y + 14z) / (18y + 24z) = 1/10
90y + 140z = 18y + 24z
72y = 116z
y/z = 116/72
y/z = 29/18

Conclusion:
- Therefore, R takes 18 hours to fill the tank individually.
Community Answer
There are three taps P, Q and R. P takes thrice as much time as Q and ...
R will take 24h
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There are three taps P, Q and R. P takes thrice as much time as Q and R together to fill a tank. Q takes twice as much time as P and R together to fill the tank. In how much time (in hours) can R fill the tank individually, if the three together require 10 hours to fill the tank when opened simultaneously?
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There are three taps P, Q and R. P takes thrice as much time as Q and R together to fill a tank. Q takes twice as much time as P and R together to fill the tank. In how much time (in hours) can R fill the tank individually, if the three together require 10 hours to fill the tank when opened simultaneously? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about There are three taps P, Q and R. P takes thrice as much time as Q and R together to fill a tank. Q takes twice as much time as P and R together to fill the tank. In how much time (in hours) can R fill the tank individually, if the three together require 10 hours to fill the tank when opened simultaneously? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are three taps P, Q and R. P takes thrice as much time as Q and R together to fill a tank. Q takes twice as much time as P and R together to fill the tank. In how much time (in hours) can R fill the tank individually, if the three together require 10 hours to fill the tank when opened simultaneously?.
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