A train 300 m long passed a man walking along the line in the same direction at the rate of 3 km/hr in 33 sec. The speed of the train is :

Solution (By Examveda Team)

Let the speed of train = $$x$$ km/hr
Length of train = 300 mitres
Their relative speed in same direction :
= ($$x$$ - 3) km/hr
According to the question,
$$\frac{{\left( {300 + 0} \right){\text{m}}}}{{\left( {x - 3} \right) \times \frac{5}{{18}}{\text{ m/s}}}} = 33$$
[Here man's length is 0 metre]
$$\eqalign{ & \Rightarrow \frac{{300 \times 18}}{{\left( {x - 3} \right) \times 5}} = 33 \cr & \Rightarrow \frac{{100 \times 18}}{{5x \times 15}} = 11 \cr & \Rightarrow 1800 = 55x - 165 \cr & \Rightarrow 55x = 1965 \cr} $$
∴ Speed of the train :
$$\eqalign{ & \Rightarrow x = \frac{{1965}}{{55}} \cr & \Rightarrow x = 35\frac{8}{{11}}{\text{ km/hr}} \cr} $$