lf A and B work together, they will complete a task in 10 days. If B and C work together, the task will be over in 15 days and if C and A work together, they will complete the same task in 12 days. When will the task be completed if all three work together and how long will each of them working alone, take to complete the job?

Explanation:

A + B take 10 days …(1)

B + C take 15 days …(2)

A +1C take 12 days …(3)

i.e. 1\A+1\B=1\10 …(1)

1\B+1\C=1\15 …(2)

1\C+1\A=1\12 …(3)

Adding (1), (2) and (3) we get, 2(1\A+1\B+1\C)=1\10+1\15+1\12=1\4

or 1\A+1\B+1\C=1\8 …(4)

or A, B and C working together will take 8 days to complete the job.

Subtracting(1), (2) and (3) from (4) we get the individual time taken by A, B and C which are 120\7 days, 24 days and 40 days respectively.