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C’s share of the earnings

by sanju09 » Tue Apr 05, 2011 3:57 am
A, B and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $2340, what will be C's share of the earnings?
(A) $520
(B) $630
(C) $1000
(D) $1080
(E) $1170
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by Anurag@Gurome » Tue Apr 05, 2011 4:05 am
sanju09 wrote:A, B and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $2340, what will be C's share of the earnings?
(A) $520
(B) $630
(C) $1000
(D) $1080
(E) $1170
1 day work of A, B, and C is 1/6, 1/8, and 1/12 respectively.
This means A:B:C = 1/6:1/8:1/12
LCM of 6, 8, 12 = 24
So, A:B:C = 24/6:24/8:24/12 = 4:3:2
Hence, 4x + 3x + 2x = 2340
9x = 2340 implies x = $260, which implies C's share = 2 * $260 = $520

The correct answer is A.
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by vineeshp » Tue Apr 05, 2011 4:07 am
A 520.

Working together, they finish 3/8 ( = 1/6 + 1/8 + 1/12) of work in one day. Or in other words, they can finish the work in 8/3 days.

This means when they work together, each machine works for 8/3 days. C working at speed of 1/12 finishes 8/3 * 1/12 = 2/9 of the total work.

So money earned = 2/9 * 2340 = 520.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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