Working together, A and B can do a job in 6 days; B and C can do the same job in 10 days, while C and A will take 7.5 days to do the same. lf all three A, B and C work together when will they complete the job?

Explanation:

Working alone let A take ‘a’ days to complete the job; similarly, let B take ‘b’ days and

C take ‘c’ days.

Working together, A and B take 6 days. i.e., they complete 1\6th of the job in a day.

Or 1\a+1\b=1\6 …eqn(1)

Similarly, B and C will complete

=1\b+1\b=1\10th of the job in a day. …eqn (2)

And C and A will complete 1\c+1\a=1\7.5

= 2\15 of the job in a day …eqn (3)

Addinq (1), (2) and (3), we get

1\a+1\b+1\b1\c+1\c+1\a=2\a+2\b+2\c=1\6+1\10+2\15

Or 2(1\a+1\b+1\c)=5+3+4\30=4\10=2\5

Or 1\a+1\b+1\c=1\5 …eqn(4)

i.e. working together, A, B and C complete 1/5th of the job in a day.

Therefore, they will complete the job in 5 days.

Subtracting eqn (1)from eqn (4) we get 1\a+1\b+1\c−(1\a+1\b)=1\c=1\5−1\6=1\30

or C takes 30 days. 1\a+1\b+1\c−(1\b+1\c)=\1a=1\5−1\10=1\30 or A takes 10 days.

1\a+1\b+1\c−(1\c+1\a)=1\b=1\5−2\15=1\15 or B takes 15 days