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 :

Answer: Option D

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]
$$\begin{array}{rl}& \Rightarrow \frac{300\times 18}{\left(x-3\right)\times 5}=33\\ & \Rightarrow \frac{100\times 18}{5x\times 15}=11\\ & \Rightarrow 1800=55x-165\\ & \Rightarrow 55x=1965\end{array}$$
∴ Speed of the train :
$$\begin{array}{rl}& \Rightarrow x=\frac{1965}{55}\\ & \Rightarrow x=35\frac{8}{11}\text{ km/hr}\end{array}$$