# A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A. 45 km/hr

B. 50 km/hr

C. 54 km/hr

D. 55 km/hr

### Solution(By Examveda Team)

\eqalign{ & {\text{Speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{relative}}\,{\text{to}}\,{\text{man}} \cr & = {\frac{{125}}{{10}}} {\text{ m/sec}} \cr & = {\frac{{25}}{2}} {\text{ m/sec}} \cr & = {\frac{{25}}{2} \times \frac{{18}}{5}} {\text{ km/hr}} \cr & = 45\,{\text{km/hr}} \cr & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{train}}\,{\text{be}}\,x\,{\text{km/hr}}. \cr & \text{Then, relative speed} = \left( {x - 5} \right)\,{\text{km/hr}} \cr & \therefore x - 5 = 45 \cr & \Rightarrow x = 50\,{\text{km/hr}} \cr}

1. How did you guys assuming that 18/5 there is no 18 in question...

2. Short Trick
whenever the speed of train with respect to man/ objects moving in the same direction asked.
Just multiply the speed of man/object with time given in question .

According to question we have 10*5 =50km/hr
Be carefull with units .

3. Short trick is that just multiply the time and speed of man which gives speed of train

4. we know that,
S=D/T
X-5=125*18/5/9=50

5. the train and the man is moving in same direction. So the relative speed = (speed of train-speed of man). Consider the train speed as x.
we know that,
Distance/Speed=Time
Length of train=125m
Speed of man=5 km/hr=5*5/18=25/18 m/s.
time=10s
now,
125/(x-25/18)=10
125*18=(18x-25)10
2250=180x-250
2500=180x
x=250/18
the ans is in km/hr. To convert m/s -> km/hr multiply the ans by 18/5
Therefore, (250/18)*(18/5)= 50 km/hr
Ans option B.
Hope you understand.

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