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 = ?

Solution(By Examveda Team)

$$\eqalign{ & \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{6} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{8} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{{12}}{\text{ }} \cr & \therefore \left( {{\text{A}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {2 \times \frac{1}{6}} \right) - \left( {\frac{1}{8} + \frac{1}{{12}}} \right) \cr & = \left( {\frac{1}{3} - \frac{5}{{24}}} \right) \cr & = \frac{3}{{24}} \cr & = \frac{1}{8} \cr} $$
So, A and C together will do the work in 8 days.