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10 May 2015, 12:04
Kudos
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B
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Difficulty:
35%
(medium)
Question Stats:
71% (01:57) correct
29%
(02:18)
wrong
based on 242
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If 16 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -third less time?
a. 4
b. 8
c. 10
d. 12
e. 16
a. 4
b. 8
c. 10
d. 12
e. 16
10 May 2015, 13:13
Kudos
Bookmarks
You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.
We can solve this problem identically. If 16 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 16*36 machine-days of work. So the job requires 16*36 days of machine work in total. We instead want the job done in 1/3 less time, so in 24 days. So we'll need 16*36/24 = 24 machines, or 8 additional machines.
We can solve this problem identically. If 16 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 16*36 machine-days of work. So the job requires 16*36 days of machine work in total. We instead want the job done in 1/3 less time, so in 24 days. So we'll need 16*36/24 = 24 machines, or 8 additional machines.
General Discussion
10 May 2015, 20:28
Kudos
Bookmarks
Hi,
16 machines can finish a JOB in 36 days.
Let me re frame the sentence here:
In 36 days 16 machines can finish a JOB.
In 1 day 16 machines can finish (1/36) part of JOB
In 1 day 1 machine can finish 1/(36*16) part of JOB---------------------------- (1)
We know that the JOB has to be completed in one-third less time which means 36-1/3*(36) = 24 days
From (1)
In 24 days 1 machine can finish 24/(36*16) part of JOB i.e. 1/24 part of JOB
So you need 24 machines to finish the JOB in 24 days.
So number of extra machines that you need is 24 -16 = 8
Answer B
Hope the explanation is clear!
Consider giving Kudos
Ambarish
16 machines can finish a JOB in 36 days.
Let me re frame the sentence here:
In 36 days 16 machines can finish a JOB.
In 1 day 16 machines can finish (1/36) part of JOB
In 1 day 1 machine can finish 1/(36*16) part of JOB---------------------------- (1)
We know that the JOB has to be completed in one-third less time which means 36-1/3*(36) = 24 days
From (1)
In 24 days 1 machine can finish 24/(36*16) part of JOB i.e. 1/24 part of JOB
So you need 24 machines to finish the JOB in 24 days.
So number of extra machines that you need is 24 -16 = 8
Answer B
Hope the explanation is clear!
Consider giving Kudos
Ambarish
