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?

Question

Zoe Adams · Accepted Answer

C's share in earnings will be #$520#.

As A, B and C, each working alone complete a job in #6#, #8# and #12# days, respectively, they do #1/6#, #1/8# and #1/12# of the job in a day. Hence they together do #1/6+1/8+1/12=4/24+3/24+2/24=9/24=3/8# of the job in one day or complete the job in #8/3=2 2/3# days. Note that work done by them is in the ratio #1/6:1/8:1/12hArr4/24:3/24:2/24hArr4:3:2#. As the work done by them is in the ratio of #4:3:2# (their sum is #4+3+2=9#), C's share in earnings will be #$2340xx2/9=260cancel(2340)xx2/(1cancel9)=$520#.

Everly Taylor · Answer

undefined To find C's share of the earnings, first, calculate the rates at which each person completes the job per day (i.e., their individual work rates).

A's work rate = 1/6 job per day
B's work rate = 1/8 job per day
C's work rate = 1/12 job per day

When they work together, their combined work rate per day is the sum of their individual work rates.

Combined work rate = 1/6 + 1/8 + 1/12 = (4/24) + (3/24) + (2/24) = 9/24 = 3/8 job per day

Now, determine how many days it takes for them to complete the job together.

Total job = 1
Total days to complete the job together = 1 / (3/8) = 8/3 days

Now, find C's share of the earnings:

C's share = (C's work rate) × (total days worked by C) × (total earnings per day)
          = (1/12) × (8/3) × ($2340 / (6 + 8 + 12))
          = (8/36) × ($2340 / 26)
          = (2/9) × $90
          = $20

So, C's share of the earnings is $20.