A can do a piece or work in 6 days. B in 8 days and C in 12 days. B and C together worked for 2 days and then C is replaced by A. Find when the work will be finished.

Explanation:

A can do the work in 6 days.

A’s one day work = 1\6 part.

B’s one day work = 1\8 part

C’s one day work = 1\12 part

(B+C)’s one day work = 1\8+1\12=3+2\24=5\24

(B+C)’s 2 day work = 5\24×2=5\12

Remaining work = 1−5\12=7\12

Remaining work is done by A and B

(A+B)’s one day work = 1\6+1\8=4+3\24=7\24

7\12 part of work can be done by

A and B in = 7\12×24\7=2 days

The work is completed in 2+2 = 4 days.