A can do a piece of work in = 24 days
(A + B) can do a piece of work in = 16 days
(A + B + C) can do a piece of work in = 10. 2/3 days = 32/3 days
∴ A’s 1 day work = 1/24
(A + B)’s 1 day work = 1/16
(A + B + C)’s 1 day work = 3/32
C’s 1 day work = 3/32 – 1/16
= (3 – 2)/32 = 1/32
(A + C)’s 1 day work = 1/24 + 1/32
= (4 + 3)/96 = 7/96
∴ (A + C) can do the work in = 96/7 days
= 13. 5/7 days