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02 Dec 2020, 08:00
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C
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Difficulty:
55%
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Question Stats:
69% (02:28) correct
31%
(02:45)
wrong
based on 108
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There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?
A. 5
B. 6
C. 7
D. 8
E. 9
Are You Up For the Challenge: 700 Level Questions
A. 5
B. 6
C. 7
D. 8
E. 9
Are You Up For the Challenge: 700 Level Questions
02 Dec 2020, 08:37
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Bunuel
There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?
A. 5
B. 6
C. 7
D. 8
E. 9
A. 5
B. 6
C. 7
D. 8
E. 9
Let the number of fill pipes = x
Therefore the number of drain pipes = 12 - x
Time taken by 1 fill pipe = 8 hours
Work done by 1 fill pipe in 1 hour = \(\frac{1}{8}\)
Work done by x fill pipes in 1 hour = \(x * \frac{1}{8} = \frac{x}{8}\)
Time taken by 1 drain pipe to empty = 6 hours
Work done by 1 drain pipe in 1 hour = \(\frac{1}{6}\)
Work done by x fill pipes in 1 hour = \((12 - x) * \frac{1}{8} = \frac{12 - x}{8}\)
Total time to fill the tank = 24 hours.
Amount filled in 1 hour = \(\frac{1}{24}\)
Therefore \(\frac{x}{8} - \frac{12 - x}{6} = \frac{1}{24} \)
\(\frac{3x - 4(12 - x)}{24} = \frac{1}{24}\)
3x - 48 + 4x = 1
7x = 49
x = 7
Option C
Arun Kumar
02 Dec 2020, 09:22
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Bunuel
There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?
A. 5
B. 6
C. 7
D. 8
E. 9
Are You Up For the Challenge: 700 Level Questions
A. 5
B. 6
C. 7
D. 8
E. 9
Are You Up For the Challenge: 700 Level Questions
Let the capacity of the tank = LCM of 8, 6 and 24 = 24 liters
Filling rate of each pipe = 24/8 = 3 liters per hour
Emptying rate of each pipe = 24/6 = 4 liters per hour
Effective rate of filling considering all pipes together = 24/24 = 1 liter per hour
Assuming n fill pipes and (12-n) emptying pipes, we have: 3n - 4(12-n) = 1
=> 7n = 49
=> n = 7
Answer C
