A can build a wall in the same time in which B and C together can do it. If A and B together can do it. If A and B together could do it in 25 days and C alone in 35 days, in what time could B alone do it ?

Solution(By Examveda Team)

$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} = \frac{1}{{25}} \cr & {\text{C's 1 day's work}} = \frac{1}{{35}} \cr & \left( {{\text{A}} + {\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{25}} + \frac{1}{{35}}} \right) \cr & = \frac{{12}}{{175}}.....({\text{i}}) \cr} $$
Also, A's 1 day's work = (B + C)'s 1 day's work.....(ii)
$$\eqalign{ & {\text{From (i) and (ii), we get : }} \cr & \Rightarrow {\text{2}} \times \left( {{\text{A's 1 day's work}}} \right) = \frac{{12}}{{175}} \cr & \Rightarrow {\text{A's 1 day's work}} = \frac{6}{{175}} \cr & \therefore {\text{B's 1 day's work}} \cr & = \left( {\frac{1}{{25}} - \frac{6}{{175}}} \right) \cr & = \frac{1}{{175}} \cr} $$