Question

A train $ 125{\text{ m}} $ long passes a man, running at $ 5{\text{ km/hr}} $ in the same direction in which the train is going, in $ 10 $ second. The speed of the train is:
A. $ 45{\text{ km/hr}} $
B. $ 50{\text{ km/hr}} $
C. $ 54{\text{ km/hr}} $
D. $ 55{\text{ km/hr}} $

Answer 1

Hint:
Here we know the train's length along with man’s speed of running. But he is running along with the train in the same direction and we know that in $ 10 $ seconds the train passes the man. So firstly we can let the man be still and find the speed of the train relative to man. This speed which we will get will be the speed relative to the man but we need the actual speed of the train which will be $ 5{\text{ km/hr}} $ more than this speed as man is also running in the same direction with the speed of $ 5{\text{ km/hr}} $

Complete step by step solution:
Here we are given that a train $ 125{\text{ m}} $ long passes a man, running at $ 5{\text{ km/hr}} $ in the same direction in which the train is going, in $ 10 $ second.
So the train’s speed relative to man $ = \dfrac{{{\text{distance(length of the train)}}}}{{{\text{time taken}}}} $
So speed relative to man $ = \dfrac{{125}}{{10}} = \dfrac{{25}}{2}{\text{m/sec}} $
We can convert it into the $ {\text{km/hr}} $ as we know that $ 1{\text{m}} = \dfrac{1}{{1000}}{\text{km and 1sec = }}\dfrac{1}{{3600}}{\text{hr}} $
So we get that
 $ \dfrac{{25}}{2}{\text{m/sec = }}\dfrac{{25 \times \dfrac{1}{{1000}}}}{{2 \times \dfrac{1}{{3600}}}} = \dfrac{{25}}{2} \times \dfrac{{3600}}{{1000}} = \dfrac{{25}}{2} \times \dfrac{{36}}{{10}} = 45{\text{km/hr}} $
So this is the speed we have got which is the speed of the train with respect to the man which is $ 45{\text{km/hr}} $
But the man is also running with the same train in the same direction in which the train is moving. So we can say that the actual speed of the train would be $ 5{\text{km/hr}} $ more than that of the speed of the train relative to the man.
So we can say speed of the train $ = (45 + 5){\text{km/hr}} = 50{\text{km/hr}} $

Hence B is the correct option.

Note:
Here if the man would be running in the opposite direction to that of the train then we would have subtracted his speed from the $ 45{\text{km/hr}} $ as the actual speed of the train would be less than what he felt when he was moving in the opposite direction.