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22 Apr 2020, 06:13
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D
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Difficulty:
25%
(medium)
Question Stats:
81% (01:53) correct
19%
(02:14)
wrong
based on 101
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A, working alone, can complete a job in 12 hours and B, working alone, can complete the job in 18 hours. If A and B work on the job in alternate hours starting with A, in how much time will the job be done?
A. 13
B. 13 hours and 20 minutes
C. 14 hours
D. 14 hours and 20 minutes
E. 15 hours
Are You Up For the Challenge: 700 Level Questions
A. 13
B. 13 hours and 20 minutes
C. 14 hours
D. 14 hours and 20 minutes
E. 15 hours
Are You Up For the Challenge: 700 Level Questions
Chethan92
Joined: 18 Jul 2018
Last visit: 21 Apr 2022
Posts: 903
Own Kudos:
Given Kudos: 95
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy)
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22 Apr 2020, 06:51
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A takes 12 hours.
B takes 18 hours.
LCM of work to be done = (12,18) = 36 units
A can do 3 units/hour.
B can do 2 units/hour.
In 2 hours, A+B = 5 units
Multiply by 7, then 14 hours, 35 units are done.
Next, A can do 3 units in 60 min. or 1 unit in 20 min.
Hence the work will be completed in 14hours 20 min.
D is the answer.
B takes 18 hours.
LCM of work to be done = (12,18) = 36 units
A can do 3 units/hour.
B can do 2 units/hour.
In 2 hours, A+B = 5 units
Multiply by 7, then 14 hours, 35 units are done.
Next, A can do 3 units in 60 min. or 1 unit in 20 min.
Hence the work will be completed in 14hours 20 min.
D is the answer.
22 Apr 2020, 14:58
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Bunuel
if A starts working first, then A will work 7 hours and B will work 6 hours: (13 hours )
\(1 -7(\frac{1}{12}) - 6(\frac{1}{18})= \frac{36- 21- 12}{ 36}= \frac{3}{36} = \frac{1}{12}\) (amount of work left to be done)
\(\frac{1}{12} > \frac{1}{18}\)
So, B will have to work an hour again: (1 hour)
\(\frac{1}{12} - \frac{1}{18} = \frac{1}{36}\) (remaining amount of work)
\(\frac{1}{36} < \frac{1}{12} \)
So, \(x(\frac{1}{12}) = \frac{1}{36} \)
--> \(x = \frac{1}{3}\) hour = \(\frac{60}{3}\) = \(20\) minutes
In total, 13hours + 1 hour + 20 minutes = 14 hours 20 minutes
Answer (D)
