SOLUTION: A B and C can do a piece of work i. 8 9 10 days respectively. They all work together and completed a job that fetched rs 3630. Find the share of each

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Question 1103810: A B and C can do a piece of work i. 8 9 10 days respectively. They all work together and completed a job that fetched rs 3630. Find the share of each
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2F8+%2B+1%2F9+%2B+1%2F10+=+1%2Ft+
+45%2F360+%2B+40%2F360+%2B+36%2F360+=+1%2Ft+
+121%2F360+=+1%2Ft+
Their shares will be proportional to
their respective +1%2Ft+ values
---------------------------------
A's share:
++%28%28+45%2F360+%29+%2F+%28+121%2F360+%29%29%2A3630+
+%28+45%2F121+%29%2A3630+=+30%2A45+
+30%2A45+=+1350+
----------------------------------
B's share:
+%28%28+40%2F360+%29+%2F+%28+121%2F360+%29%29%2A3630+
+%28+40%2F121+%29%2A3630+=+40%2A30+
+40%2A30+=+1200+
----------------------------------
C's share:
+%28%28+36%2F360+%29%2F%28+121%2F360+%29%29%2A3630+
+%28+36%2F121+%29%2A3630+=+36%2A30+=+1080+
-----------------------------------
Their shares are:
A: rs 1,350
B: rs 1,200
C: rs 1,080
-------------
check:
+A+%2B+B+%2B+C+=+1350+%2B+1200+%2B+1080+
+A+%2B+B+%2B+C+=+3630+
OK
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Feel free to get a 2nd opinion on this!


Answer by ikleyn(52862) About Me  (Show Source):
You can put this solution on YOUR website!
.
A B and C can do a piece of work i. 8 9 10 days respectively. They all work together and completed a job that fetched rs 3630.
Find the share of each
~~~~~~~~~~~~~~~~~~~~~~~~ 

Their rates of work are : 

    A:  1%2F8  of the job per day;

    B:  1%2F9  of the job per day;

    C:  1%2F10  of the job per day.


If they completed the job in "t" days, then

   t%2F8 + t%2F9 + t%2F10 = 1,   or

   %289%2A10%2At%29%2F%288%2A9%2A10%29 + %288%2A10%2At%29%2F%288%2A9%2A10%29 + %288%2A9%2At%29%2F%288%2A9%2A10%29 = 1,   or

   %2890%2F720+%2B+80%2F720+%2B+72%2F720%29%2At = 1,   which implies  %28242%2F720%29%2At = 1,  or  t = 720%2F242 days.


   
It means that A  made  %2890%2F720%29%2A%28720%2F242%29 = 90%2F242 part of the entire job,

              B  made  %2880%2F720%29%2A%28720%2F242%29 = 80%2F242 part of the entire job,   and

              C  made  %2872%2F720%29%2A%28720%2F242%29 = 72%2F242 part of the entire job.


Now notice that  242 = 3630%2F15,  so every 1%2F242 part of the job costs  3630%2F242 = 15 rupees.


It means that  A should obtain  15*90 = 1350 rupees,

               B should obtain  15*80 = 1200 rupees,   and 

               C should obtain  15*72 = 1080 rupees.


Easy check:  1350 + 1200 + 1080 = 3630 rs.    ! Correct !

Solved.