If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in -

Question: If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in -

Solution:
in one day,
(A + B) do = 1/18
(A + C) do = 1/12
(B + C) do = 1/9

(A + B) + (A + C) + (B + C) = 1/18 + 1/12 + 1/9
2 (A + B + C) = 9/36 = 1/4
A + B + C = 1/8

so, B alone can do in one day = (A + B + C) - (A + C)
= 1/8 - 1/12
= 1/24

hence, it will take B to do the whole work in 24 days