A and B can do a work in = 8 days
B and C can do a work in = 12 days
A and C can do a work in = 16 days
(A+B)’s 1 day work =
(B+C)’s 1 day work =
(A + C)’s 1 day work = 1/16
∴ [(A + B) + (B + C) + (A + C)]’s 1 day work
= 1/8 + 1/12 + 1/16
i.e. [A + B + B + C + A + C]’s 1 day work
= 1/8 + 1/12 + 1/16
= (6 + 4 + 3)/48 = 13/48
i.e. 2(A + B + C)’s 1 day work = 13/48
i.e. (A + B + C)’s 1 day work = 13/48 × ½ = 13/96
∴ (A + B + C) can do the work in = 96/13 days
= 7. 5/13 days.