A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in

1. 8 days
2. 6 days
3. 4 days
4. 12 days

Solution

Assume total work to be 24 units (common multiple of 8, 12 and 6). 

A and B can do 24 units of work in 8 days. (A+B)'s one day work = 3 units

B and C can do 24 units of work in 12 days. (B+C)'s one day work = 2 units

A, B and C can do 24 units of work in 6 days. (A+B+C)'s one day work = 4 units

Multiply third equation by 2 and subtract first two equations,

2(A+B+C) - (A+B) - (B+C) = 2*4 - 3 - 2

(A+C)'s one day work = 3 units

A and C can do 24 units of work in 8 days.

The correct option is A.