A and B can do a piece of work in = 40 days
B and C can do a piece of work in = 30 days
C and A can do a piece of work in = 24 days
(A+B)’s 1 day work = 1/40
(B+C)’s 1 day work = 1/30
(C+A)’s 1 day work = 1/24
(i) [(A+B)+(B+C)+(C+A)]’s 1 day work = 1/40 + 1/30 + 1/24
= (3 + 4 + 5)/120
= 12/120 = 1/10
i.e. (A + B + B + C + C + A)’s 1 day work = 1/10
i.e. 2(A + B + C)’s 1 day work = 1/10
∴ (A + B + C)’s 1 day work = 1/10 × ½
= 1/20
∴ (A + B + C) can do the work in = 20 days
(ii) A’s 1 day work = 1/20 – 1/30
= (3 – 2)/60 = 1/60
∴ A can do the work in 60 days
B’s 1 day work = 1/20 – 1/24
= (6 – 5)/120 = 1/120
∴ B can do the work in 120 days
Now, C’s 1 day work = 1/20 – 1/40
= (2 – 1)/40 = 1/40
C can do the work in 40 days
Hence A can do the work in = 60 days
B can do the work in = 120 days
C can do the work in = 40 days