A can do a work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it?

Question: A can do a work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B take alone to do it?

Solution:
A's 1 hour work = 1/4
(B + C)'s 1 hour work = 1/3
(A + C)'s 1 hour work = 1/2

(A + B + C)'s 1 hour work = 1/4 + 1/3 = 7/12

∴ B's 1 hour work is = {(A + B + C)'s 1 hour work} - {(A + C)'s 1 hour work}
= 7/12 - 1/2
= 1/12

so, B alone can do it in 12 hours.