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

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New post 15 Mar 2016, 12:32
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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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Re: A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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New post 15 Mar 2016, 19:33
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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$
Answer A
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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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New post 15 Mar 2016, 20:12
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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

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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.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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New post 15 Mar 2016, 22:41
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
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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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New post 16 Mar 2016, 03:59
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?
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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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New post 16 Mar 2016, 04:06
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
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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


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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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New post 16 Mar 2016, 04:17
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
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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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New post 16 Mar 2016, 04:44
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
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A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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New post 17 Mar 2016, 03:13
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
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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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New post 17 Mar 2016, 03:50
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
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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


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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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New post 17 Mar 2016, 03:59
chetan2u thanks for prompt reply and a gr8 explanation
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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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New post 21 Mar 2017, 03:36
Is there a way to quickly find the ratios of 3 given numbers like above ? instead of doing time demanding lcm method..
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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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New post 27 Jun 2017, 14:47
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
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A, B and C, each working alone can complete a job in 6, 8 and 12 days  [#permalink]

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New post 27 Jun 2017, 22:38
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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