# 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

**Answer: Option B **

__Solution(By Examveda Team)__

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

## Comments ( 5 )

Related Questions on Problems on Trains

A. 120 metres

B. 180 metres

C. 324 metres

D. 150 metres

A. 45 km/hr

B. 50 km/hr

C. 54 km/hr

D. 55 km/hr

A. 200 m

B. 225 m

C. 245 m

D. 250 m

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

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 .

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

we know that,

S=D/T

X-5=125*18/5/9=50

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.