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

Question

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

chetan2u · Accepted Answer

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

Skywalker18 · Answer

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

Mathivanan Palraj · Answer

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

lillianmbula · Answer

Where are you getting that 2/9?

chetan2u · Answer

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

lillianmbula · Answer

Yes it does. Perfectly

engi17 · Answer

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

sharma123 · Answer

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

chetan2u · Answer

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

sharma123 · Answer

chetan2u  thanks for prompt reply and a gr8 explanation

mesutthefail · Answer

Is there a way to quickly find the ratios of 3 given numbers like above ? instead of doing time demanding lcm method..

sasyaharry · Answer

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

SVaidyaraman · Answer

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

krishna_sunder_ · Answer

answer =  *2340 = 520

Because 
RATE        *        TIME        =WORK
a                          6           =1
b                          8           =1
c                         12           =1

a+b+c                  x            =1

‘a’ can do 1/6 work in 1h, then  in ‘x’ hours he can complete ‘x/6’
The same way ‘b’ and ‘c’ complete ‘x/8’ and ‘x/12’
Therefore the ratio of work completed by ‘c’ is 
(x/8) %   = 2/9
U get paid for portion of work u completed
Therefore if u completed 2/9 th of the work, 
U get paid 2/9th of the total amount
Therefore the answer = (2/9) * 2340 = 520

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards