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# A, B and C, each working alone can complete a job in 6, 8 and 12 days

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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15 Mar 2016, 11:32
1
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Difficulty:

55% (hard)

Question Stats:

71% (02:23) correct 29% (02:44) wrong based on 311 sessions

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A, B and C, each 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.$1080
D. $1100 E.$1170

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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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15 Mar 2016, 19:12
5
1
Bunuel wrote:
A, B and C, each 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.$1080
D. $1100 E.$1170

Hi,

a straight method would be--

the share of work that each does would be in
1)the opposite ratio of their time taken, if only two were working
2) OR, in the ratio of product of individual time of other two .

Time take by A:B:C=6:8:12
so the share of work done by A:B:C=12*8:6*12:6*8=4:3:2..
so they will be paid in the same ratio- 4:3:2
C will get $$\frac{2}{(4+3+2)} * 2340$$ = 2*260 = 520
A

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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15 Mar 2016, 18:33
2
4
Let work done by A in a day = 1/6
work done by B in a day = 1/8
work done by C in a day = 1/12

total work done by 3 of them in a day = 1/6 + 1/8 + 1/12
= (4+3+2)/24
=9/24

Fraction of work done by C in a day= 2/9
fraction of total work by each of them will be same as the work done by each individual in a day.
Total earning on completion of job = 2340 $C's share of earning = (2/9)*2340 =520$
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##### General Discussion
Manager
Joined: 09 Jun 2015
Posts: 92
Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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15 Mar 2016, 21:41
Bunuel wrote:
A, B and C, each 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.$1080
D. $1100 E.$1170

The efficiency ratio is 1/6: 1/8: 1/12, which is equal to 4:3:2
C's share is 2340*2/9 = 520
Intern
Joined: 08 Feb 2016
Posts: 13
Concentration: Finance, General Management
Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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16 Mar 2016, 02:59
Bunuel wrote:
A, B and C, each 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.$1080
D. $1100 E.$1170

Where are you getting that 2/9?
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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16 Mar 2016, 03:06
lillianmbula wrote:
Bunuel wrote:
A, B and C, each 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.$1080
D. $1100 E.$1170

Where are you getting that 2/9?

Hi
the ratio of A:B:C = 4:3:2 ..
so C's share = $$\frac{C}{(A+B+C)} = \frac{2}{(4+3+2)}=\frac{2}{9}$$

Hope it helps
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Intern
Joined: 08 Feb 2016
Posts: 13
Concentration: Finance, General Management
Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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16 Mar 2016, 03:17
chetan2u wrote:
lillianmbula wrote:
Bunuel wrote:
A, B and C, each 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.$1080
D. $1100 E.$1170

Where are you getting that 2/9?

Hi
the ratio of A:B:C = 4:3:2 ..
so C's share = $$\frac{C}{(A+B+C)} = \frac{2}{(4+3+2)}=\frac{2}{9}$$

Hope it helps

Yes it does. Perfectly
Intern
Joined: 10 Mar 2016
Posts: 4
Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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16 Mar 2016, 03:44
1
2
Bunuel wrote:
A, B and C, each 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.$1080
D. $1100 E.$1170

IMO A. $520 The dollars earned will be in the same ratio as amount of work done 1 day work of C is 1/12 (or 2/24) 1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24 C's contribution is 2/9 of the combined effort Translating effort to$ = 2/9 * 2340 = $520 Intern Joined: 29 Oct 2014 Posts: 38 A, B and C, each working alone can complete a job in 6, 8 and 12 days [#permalink] ### Show Tags 17 Mar 2016, 02:13 chetan2u wrote: Bunuel wrote: A, B and C, each 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. $1080 D.$1100
E. $1170 Hi, a straight method would be-- the share of work that each does would be in 1)the opposite ratio of their time taken, if only two were working 2) OR, in the ratio of product of individual time of other two . Time take by A:B:C=6:8:12 so the share of work done by A:B:C=12*8:6*12:6*8=4:3:2.. so they will be paid in the same ratio- 4:3:2 C will get $$\frac{2}{(4+3+2)} * 2340$$ = 2*260 = 520 A Hi chetan2u can you please explain where im wrong. I did work done a:b:c=12:8:6 so share of c =>6/26*2340=540 Math Expert Joined: 02 Aug 2009 Posts: 7334 Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days [#permalink] ### Show Tags 17 Mar 2016, 02:50 2 sharma123 wrote: chetan2u wrote: Bunuel wrote: A, B and C, each 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. $1080 D.$1100
E. $1170 Hi, a straight method would be-- the share of work that each does would be in 1)the opposite ratio of their time taken, if only two were working 2) OR, in the ratio of product of individual time of other two . Time take by A:B:C=6:8:12 so the share of work done by A:B:C=12*8:6*12:6*8=4:3:2.. so they will be paid in the same ratio- 4:3:2 C will get $$\frac{2}{(4+3+2)} * 2340$$ = 2*260 = 520 A Hi chetan2u can you please explain where im wrong. I did work done a:b:c=12:8:6 so share of c =>6/26*2340=540 Hi, the work done would not be the opposte of time taken.. if there are two persons you can use this .. But if there are more than two, the ratio will be dependent on other two, three etc.. so share of work A:B:C= B*C : A*C : A*B, here A,B,C are tim etaken.. so the ratio = 12*8 : 12*6 : 16*8 = 96 : 72 : 48 = 24*4 : 24*3 : 24*2 = 4:3:2.. so C's share= 2/9 * 2340 = 520 _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert Intern Joined: 29 Oct 2014 Posts: 38 Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days [#permalink] ### Show Tags 17 Mar 2016, 02:59 chetan2u thanks for prompt reply and a gr8 explanation Intern Joined: 12 Dec 2016 Posts: 10 Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days [#permalink] ### Show Tags 21 Mar 2017, 02:36 Is there a way to quickly find the ratios of 3 given numbers like above ? instead of doing time demanding lcm method.. Manager Joined: 22 Nov 2016 Posts: 207 Location: United States Concentration: Leadership, Strategy GPA: 3.4 Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days [#permalink] ### Show Tags 27 Jun 2017, 13:47 1 First get the combined rate by adding the individual rates to get $$\frac{3}{8}$$ The problem tells us that working at the rate of $$\frac{3}{8}$$, the total money earned was 2340 Since C worked at $$\frac{1}{12}$$ the rate, his/her earnings will be $$\frac{2340}{12} * \frac{8}{3}$$ Now using approximation, $$\frac{2340}{12}$$ is slightly less than 200 $$200*\frac{8}{3} = \frac{1600}{3}$$ = slightly less than 530 The only answer is A _________________ Kudosity killed the cat but your kudos can save it. Director Joined: 17 Dec 2012 Posts: 624 Location: India A, B and C, each working alone can complete a job in 6, 8 and 12 days [#permalink] ### Show Tags 27 Jun 2017, 21:38 Bunuel wrote: A, B and C, each 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. $1080 D.$1100
E. $1170 1.They will share in the ratio of (1/6):(1/8):(1/12) or 8:6:4 2. C's share will be (4/18)*2340=$520
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Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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04 Sep 2018, 18:17
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Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days   [#permalink] 04 Sep 2018, 18:17
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