A and B can do a piece of work in 12 days, B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?

Solution(By Examveda Team)

$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{{12}} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{8} \cr & \left( {{\text{A}} + {\text{C}}} \right){\text{'s 1 day's work}} = \frac{1}{{62}} \cr} $$
[ (A + B)'s 1 day's work + (B + C)'s 1 day's work ] - (A + C)'s 1 day's work
$$\eqalign{ & = \frac{1}{{12}} + \frac{1}{8} - \frac{1}{6} \cr & \Rightarrow 2\left( {{\text{B's 1 day's work}}} \right) = \frac{1}{{24}} \cr & \Rightarrow {\text{B's 1 day's work}} = \frac{1}{{48}} \cr} $$
Hence, B alone can do the work in 48 days.