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07 May 2020, 10:17
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
70% (02:51) correct
30%
(03:14)
wrong
based on 207
sessions
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Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish the job?
A. 45
B. 40
C. 36
D. 32
E. 30
A. 45
B. 40
C. 36
D. 32
E. 30
07 May 2020, 10:25
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Bunuel
CONCEPT: \(\frac{Manpower*Time}{Work} = Constant\)
\(\frac{(15H+5R)*30}{1} = \frac{(5H+15R)*60}{1} \)
i.e. 15H+5R = 10H+30R
i.e. H = 5R
\(\frac{(15H+5R)*30}{1} = \frac{(15H)*T}{1} \)
\(\frac{(15H+H)*30}{1} = \frac{(15H)*T}{1} \)
\(\frac{(16H)*30}{1} = \frac{(15H)*T}{1} \)
i.e. T = 32 days
Answer: Option D
General Discussion
10 May 2020, 12:30
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Bunuel
We can let h = the rate of 5 humans and r = the rate of 5 robots.
3h + r = 1/30
and
h + 3r = 1/60
Multiplying the first equation by 3, we have:
9h + 3r = 1/10
Subtracting h + 3r = 1/60 from 9h + 3r = 1/10, we have:
8h = 5/60
h = 5/480 = 1/96
Since the rate of 5 humans is 1/96, the rate of 15 humans is 3 x 1/96 = 1/32. Therefore, it takes 15 humans 1 / (1/32) = 32 days to finish the job without any robots.
Answer: D
