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02 Dec 2020, 12:45
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (02:54) correct
25%
(03:14)
wrong
based on 178
sessions
History
Date
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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank in gallons is
A. 100
B. 110
C. 120
D. 140
E. 150
A. 100
B. 110
C. 120
D. 140
E. 150
12 Dec 2020, 06:21
Kudos
Bookmarks
Bunuel
Let us take the LCM of 20, 24 and 15 = 120
So assume we have 120 units of work to be done
Time take by pipe A = 20 minutes. Therefore work done in 1 minute = \(\frac{120}{20} = 6\)
Time take by pipe B = 24 minutes. Therefore work done in 1 minute = \(\frac{120}{24} = 5\)
Let Time take by pipe C (outlet) = x minutes. Therefore work done in 1 minute = \(\frac{120}{x}\)
Total time to fill = 15 minutes. Therefore work done in 1 minute = \(\frac{120}{15} = 8\)
Therefore 6 + 5 - \(\frac{120}{x}\) = 8
\(\frac{120}{x}\) = 11 - 8 = 3
x = 40
In 1 minute the outlet pipe empties 3 gallons.
Therefore in 40 minutes = 40 * 3 = 120 gallons
Option C
Arun Kumar
General Discussion
WarriorWithin
GMAT 1: 650 Q49 V30
Posts: 65
12 Dec 2020, 07:42
Kudos
Bookmarks
Bunuel
Statement 1 - Two pipes can fill a tank in 20 and 24 minutes. So, together they can fill a tank a in :-
\(\frac{1}{20}+\frac{1}{24} = \frac{11}{120}\),
i.e. To fill N gallons of Tank - two pipes can fill in \(\frac{120}{11}\) minutes ---------------(1)
Statement 2 - Since, the tank was filled in 15 minutes, amount of water wasted will get added to original capacity of tank.
Amount of water wasted - 15 minutes * 3 (gallons/minute) = 45 gallons
So, To fill N+45 gallons of Tank - two pipes can fill in 15 minutes --------------(2)
Comparing (1) and (2),
\(\frac{N}{N+45} =\frac{120}{11*15}\)
11N = 8N + 45*8
3N = 45*8
N = 15*8
N = 120
Hope this Helps!!
