If the wheel of the engine of a train $$4\frac{2}{7}$$ metres in circumference makes 7 revolutions in 4 seconds, then the speed (in km/hr) of the train is :

Distance covered in 4 sec :
$$\eqalign{ & = \left( {\frac{{30}}{7} \times 7} \right)m \cr & = 30\,m \cr} $$
Distance covered in 1 sec = $$\frac{{30}}{4}$$
Distance covered in 1 revolution :
$$\eqalign{ & = \left( {\frac{{30}}{4}} \right)m \cr & = \frac{{15}}{2}m \cr} $$
∴ Required speed :
$$\eqalign{ & = \left( {\frac{{15}}{2}} \right)m/s \cr & = \left( {\frac{{15}}{2} \times \frac{{18}}{5}} \right)km/hr \cr & = 27\,km/hr \cr} $$