A train moves with a speed of 30 kmph for 12 minutes and for next 8 minutes at a speed of 45 kmph. Find the average speed of the train?

$$\eqalign{ & {\text{Distance = Speed }} \times {\text{Time}} \cr & {\text{Distance covered by train with the}} \cr & {\text{speed of 30 kmph in 12 minutes is }} \cr & {\text{ = 30}} \times \frac{{12}}{{60}} = 6{\text{km}} \cr & {\text{Distance covered by the same train}} \cr & {\text{with the speed of 45 kmph in 8 minutes is }} \cr & {\text{ = 45}} \times \frac{8}{{60}} = 6{\text{km}} \cr & {\text{Average speed}} \cr & {\text{ = }}\frac{{{\text{total distance}}}}{{{\text{total time}}}}. \cr & \Rightarrow \frac{{\left( {6 + 6} \right){\text{km}}}}{{\left( {12 + 8} \right)\min }} = \frac{{12}}{{20}} \times 60 \cr & {\text{ = 36 kmph}} \cr} $$