Question

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

Answer 1

Hint: Use the concept of relative speed that is to subtract the speed of man from the assumed speed of the train ($x$), it will become $x-5$. Now us the formula of speed distance and time to calculator the value of $x$

Complete step-by-step answer:

In the question above it is given that the train passes a man, running at a speed of $5$ km per hr in the same direction in which the train is going. Therefore, to solve this question we must calculate the speed of the train with respect to man i.e. relative speed and then train’s actual speed.
So, first of all let the speed of the train be $x$ Km per hr. then as per question statement relative speed w.r.t man $= x - 5$km per hr.
So the speed of train relative to man $= \dfrac{{{\text{Distance}}}}{{{\text{time}}}}$ or $= \dfrac{{{\text{length of train}}}}{{{\text{time}}}}$
I.e. $\Rightarrow \dfrac{{125}}{{10}}$metre per second
$\Rightarrow \dfrac{{25}}{2}$Metre per second
Now Converting in terms of km per hr.
$\Rightarrow \dfrac{{25}}{2} \times \dfrac{{3600}}{{1000}}$
$\Rightarrow \dfrac{{25}}{2} \times \dfrac{{18}}{5}$ Km per hr
$\Rightarrow 45$Km per hr.
Now as mentioned above relative speed w.r.t man$= x - 5$km per hr.
Therefore, $x - 5 = 45$ $\Rightarrow x = 50$km per hr.
So, option B is the correct answer.

Note: Whenever this type of question appears, always first write down the given details and then proceed to calculate the relative speed of the train with respect to man. Once the relative speed is calculated then finding the train's speed is easy. Remember converting from m/sec to Km/hr is an important step.