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22 Apr 2020, 07:41
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C
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Difficulty:
45%
(medium)
Question Stats:
73% (03:00) correct
27%
(03:15)
wrong
based on 238
sessions
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Two pipes P and Q can fill a tank in 20 hrs and 25 hrs respectively while a third pipe R can empty the tank in 30 hrs. All the pipes are opened together for 10 hrs and then pipe R is closed.In what time the tank will be filled?
A. 400/21 hrs
B. 400/23 hrs
C. 400/27 hrs
D. 200/23 hrs
E. 200/27 hrs
Are You Up For the Challenge: 700 Level Questions
A. 400/21 hrs
B. 400/23 hrs
C. 400/27 hrs
D. 200/23 hrs
E. 200/27 hrs
Are You Up For the Challenge: 700 Level Questions
\(10( \frac{1}{20}+ \frac{1}{25} —\frac{1}{30}) = 10( \frac{17}{300}) = \frac{17}{30}\) ( Amount of work done within 10 hours)
\(1 —\frac{17}{30} = \frac{13}{30}\) (remaining amount of work)
—>\(x*(\frac{1}{20} + \frac{1}{25}) = \frac{13}{30}\)
—> \(x= (\frac{13}{30})(\frac{100}{9}) = \frac{130}{27}\) (amount of time to finish the remaining amount of work with both pipes P and Q)
In total, \(10 + \frac{130}{27} = \frac{400}{27}\) hours
Answer (C)
Posted from my mobile device
\(1 —\frac{17}{30} = \frac{13}{30}\) (remaining amount of work)
—>\(x*(\frac{1}{20} + \frac{1}{25}) = \frac{13}{30}\)
—> \(x= (\frac{13}{30})(\frac{100}{9}) = \frac{130}{27}\) (amount of time to finish the remaining amount of work with both pipes P and Q)
In total, \(10 + \frac{130}{27} = \frac{400}{27}\) hours
Answer (C)
Posted from my mobile device
General Discussion
22 Apr 2020, 08:15
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Amount of work to be done = LCM(20,25,30) = 300 units.
P can do 15 units/hr
Q can do 12 units/hr
R can do 10 units/hr
Together they can do 15+12-10 = 17 units/hr
10 hr = 170 units.
Now, only P and Q work. They can fill 27 units/hr.
remaining is 130/27.
Total time is 130/27+10 = 400/27 hours.
C is the answer.
P can do 15 units/hr
Q can do 12 units/hr
R can do 10 units/hr
Together they can do 15+12-10 = 17 units/hr
10 hr = 170 units.
Now, only P and Q work. They can fill 27 units/hr.
remaining is 130/27.
Total time is 130/27+10 = 400/27 hours.
C is the answer.
