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Difficulty:
55%
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Question Stats:
69% (02:56) correct
31%
(03:15)
wrong
based on 234
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A tank can be filled by Pipe1 in 7 hours and by Pipe2 in 5 hours. There is a waste pipe which is kept open when Pipe2 is working; the tank then takes 8 hours 30 minutes to fill. What is the time taken to fill the tank if all the three pipes are working?
A)3 hours 20 minutes
B)3 hours 50 minutes
C)4 hours 15 minutes
D)4 hours 50 minutes
E)5 hours 30 minutes
A)3 hours 20 minutes
B)3 hours 50 minutes
C)4 hours 15 minutes
D)4 hours 50 minutes
E)5 hours 30 minutes
Posts: 4,849
Time taken by Pipe 1 to fill the tank = 7 hours
Amount filled in 1 hour = \(\frac{1}{7}\)
Time taken by Pipe 2 and the waste pipe to fill the tank = 8.5 hours
Amount filled in 1 hour = \(\frac{1}{8.5} = \frac{10}{85} = \frac{2}{17}\)
Net work done in 1 hour when all are working = \(\frac{1}{7} + \frac{2}{17} = \frac{17 \space + \space 14}{119} = \frac{31}{119}\)
Therefore time taken to fill the tank = \(\frac{119}{31} = 3.84\) hours
To convert 0.84 hours in minutes, we multiply by 60 = 60 * 0.84 = 50.4 minutes
Total time taken is 3 hours and 50 minutes.
Option B
Arun Kumar
Amount filled in 1 hour = \(\frac{1}{7}\)
Time taken by Pipe 2 and the waste pipe to fill the tank = 8.5 hours
Amount filled in 1 hour = \(\frac{1}{8.5} = \frac{10}{85} = \frac{2}{17}\)
Net work done in 1 hour when all are working = \(\frac{1}{7} + \frac{2}{17} = \frac{17 \space + \space 14}{119} = \frac{31}{119}\)
Therefore time taken to fill the tank = \(\frac{119}{31} = 3.84\) hours
To convert 0.84 hours in minutes, we multiply by 60 = 60 * 0.84 = 50.4 minutes
Total time taken is 3 hours and 50 minutes.
Option B
Arun Kumar
General Discussion
yashikaaggarwal
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Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,095
Let the tank capacity = 595 liters
A Pipe fill tank in 7 hours
so per hour speed = 85liter/hour
B Pipe fill tank in 5 hours
so per hour speed = 119liter/hour
The drainage pipe C and Inlet Pipe B fill tank in 8.5 hours
so they fill 595/8.5 = 70 liter / hour
B-C = 70
119-C = 70
C = 49
so C empty 49 liter per hour
A, B and C per hour working rate =
85+119-49 = 85+70 = 155 liter/hour
Working together
A,B,C can fill 595 liter tank in : 595/155 = 3.83 hours or 3 hours and 50 minutes
Answer is B
_________________
A Pipe fill tank in 7 hours
so per hour speed = 85liter/hour
B Pipe fill tank in 5 hours
so per hour speed = 119liter/hour
The drainage pipe C and Inlet Pipe B fill tank in 8.5 hours
so they fill 595/8.5 = 70 liter / hour
B-C = 70
119-C = 70
C = 49
so C empty 49 liter per hour
A, B and C per hour working rate =
85+119-49 = 85+70 = 155 liter/hour
Working together
A,B,C can fill 595 liter tank in : 595/155 = 3.83 hours or 3 hours and 50 minutes
Answer is B
_________________
Posts: 3,651
Given
To Find
• The time taken to fill the tank if all the three pipes are working.
Approach and Working Out
Correct Answer: Option B
_________________
- • A tank can be filled by Pipe1 in 7 hours and by Pipe2 in 5 hours.
• There is a waste pipe that is kept open when Pipe2 is working; the tank then takes 8 hours 30 minutes to fill.
To Find
• The time taken to fill the tank if all the three pipes are working.
Approach and Working Out
- • Pipe 1 takes 7 hours and pipe 2 takes 5 hours.
• Pipe 2 and waste pipe takes 8.5 hours.
• Let us take the total capacity as a common multiple of 5 and 8.5 which is 85.
- o Pipe 2, 17 units/hour
o Pipe 2 and the waste pipe, 10 units/hour
o The waste pipe will take out 7 units/hour.
• Pipe 1 will fill \(\frac{85}{7}\) units per hour.
• Total input/hour = Pipe 1 + Pipe 2 – Waste pipe.
- o = \(\frac{85}{7} \)+ 17 – 7
o = \(\frac{155}{7}\)
• Total time = \(\frac{85}{(155/7) }\)= \(\frac{595}{155}\) = 3.84
- o = 3 hours 50 minutes (approx)
Correct Answer: Option B
_________________
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Posts: 29
kawal27
I would attempt this with reasoning.
Pipe 1 fills in 7 hours. If there were two pipes like 1, they will fill the tank in 3.5 hours (3 hours 30 minute). Since the combination of Pipe 2 & Drain pipe fills at 8.5 hours, I would consider that the answer would have to be just a little bit over 3 hours 30 minutes.
This narrows the answer choices to (B), (C) and may be (D).
Similar logic the other way - If two pipes of the same strength as (pipe 2+ drain pipe) were filling the tank, the tank will be filled in half the time i.e. 4 hours 15 minutes. Since pipe A is faster than this combination, the answer has to be less than 4 hours 15 minutes (which is choice C)
Only (B) remains. I would mark (B) without calculation.
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