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08 Aug 2024, 13:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
62% (03:35) correct
38%
(03:29)
wrong
based on 140
sessions
History
Date
Time
Result
Not Attempted Yet
Three pipes P, Q and R fill a cistern. P & Q can fill it in 8 and 6 hours respectively. R can empty it in 9 hours. P, Q and R are opened at 1 PM, 3 PM and 3:15 PM respectively. At what time will the cistern be full?
A. 6:00 PM
B. 6:15 PM
C. 6:30 PM
D. 6:45 PM
E. 7:00 PM
A. 6:00 PM
B. 6:15 PM
C. 6:30 PM
D. 6:45 PM
E. 7:00 PM
08 Aug 2024, 17:50
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Bunuel
Taking LCM from given data for P Q and R for assuming capacity of cistern as 72 units
Efficiency for P Q and R are p q and r respectively.
\(p = 72/8 = 9 units/hr,\)
\(q = 72/6 = 12 units/hr,\)
\(r = 72/9 = -8 units/hr \) (This is draining pipe) efficiency while filling will be in terms of -ve.
Total efficiency while working together = 9+12-8 = 13units/Hr
P, Q and R are opened at 1 PM, 3 PM and 3:15 PM respectively.
Means pipe P worked alone for 2Hrs.
Then Pipe P and Q worked together for 15 mins \(= \frac{1}{4} Hrs\)
and then till 4PM all three worked together for 45 mins \(= \frac{3}{4} Hrs\)
Therefore,
Units of water filled in the cistern till 4PM \(= 2*p + \frac{1}{4}*(p+q) + \frac{3}{4}*(p+q+r) = 2*9 + \frac{1}{4}*21 + \frac{3}{4}*13 = 18 + 15 = 33 units\)
Now lets assume cistern took additional x hours for filling rest of tank \(= 72-33 = 39 units\)
Therefore, \(x = 39/13 = 3 Hrs.\)
additional 3Hrs after 4PM.
Answer is E.
08 Aug 2024, 18:25
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To solve the problem, let's break it down:
Pipe P starts at 1 PM and works alone for 2 hours until 3 PM. In 2 hours, P fills
2×9=18
2×9=18 units of water.
Pipe Q joins at 3 PM. Together, P and Q fill
9+12=21
9+12=21 units/hour. They work together for 15 minutes (0.25 hours), so they fill
0.25×21=5.25
0.25×21=5.25 units.
Pipe R starts at 3:15 PM. Now, P, Q, and R together fill
9+12−8=13
9+12−8=13 units/hour. They work together for 45 minutes (0.75 hours), filling
0.75×13=9.75
0.75×13=9.75 units.
By 4 PM, the total water filled is
18+5.25+9.75=33
18+5.25+9.75=33 units.
The remaining 39 units require
39/13=3 hours to fill. Therefore, the cistern will be full at 7 PM.
Pipe P starts at 1 PM and works alone for 2 hours until 3 PM. In 2 hours, P fills
2×9=18
2×9=18 units of water.
Pipe Q joins at 3 PM. Together, P and Q fill
9+12=21
9+12=21 units/hour. They work together for 15 minutes (0.25 hours), so they fill
0.25×21=5.25
0.25×21=5.25 units.
Pipe R starts at 3:15 PM. Now, P, Q, and R together fill
9+12−8=13
9+12−8=13 units/hour. They work together for 45 minutes (0.75 hours), filling
0.75×13=9.75
0.75×13=9.75 units.
By 4 PM, the total water filled is
18+5.25+9.75=33
18+5.25+9.75=33 units.
The remaining 39 units require
39/13=3 hours to fill. Therefore, the cistern will be full at 7 PM.
