Anuj and Manoj can together paint their house in 30 days. After working for 20 days, Anuj has to go out and Manoj finished the remaining working the next 30 days. If Manoj had gone away after 20 days instead of Anuj, then Anuj would have completed the remaining work in ?

$$\eqalign{ & \left( {{\text{Anuj}} + {\text{Manoj}}} \right){\text{'s 20 day's work}} \cr & = \left( {\frac{1}{{30}} \times 20} \right) \cr & = \frac{2}{3} \cr & {\text{Remaining work}} \cr & = \left( {1 - \frac{2}{3}} \right) \cr & = \frac{1}{3} \cr & {\text{Manoj's 30 day's work}} = \frac{1}{3} \cr & \therefore {\text{Manoj's 1 day's work}} = \frac{1}{{90}} \cr & {\text{Anuj's 1 day's work}} \cr & = \left( {\frac{1}{{30}} - \frac{1}{{90}}} \right) \cr & {\text{ = }}\frac{2}{{90}} \cr & = \frac{1}{{45}} \cr} $$
If Manoj had gone away after 20 days, then the remaining $$\frac{1}{3}$$ work would have been done by Anuj.
$$\frac{1}{{45}}$$ work is done by Anuj in 1 day
$$\frac{1}{3}$$ work would be done by Anuj in
$$\eqalign{ & = \left( {45 \times \frac{1}{3}} \right) \cr & = {\text{15 days}} \cr} $$