Question

A $100$ meter long train is running at the speed of $30km/hr$ . How much time is taken by it to pass a man standing near the railway line?
(A) $10\sec$
(B) $11\sec$
(C) $12\sec$
(D) $20\sec$

Answer 1

Hint : For solving this particular question, we have to use the relationship between metres and kilometres that is $1km = 1000m$ , we just have to apply $v = \dfrac{d}{t}$
Where ,
‘v’ is the speed in meters per second ,
‘d’ is the distance travelled by train in meters ,
And ‘t’ is the time taken by train to cover the distance in seconds .

Complete Step By Step Answer:
It is given that, the speed of train , $v = 30km/hr$ ,
And the length of the train, $d = 100m...............(1)$
For crossing a man who is standing near the railway line, the train has to cover a distance equal its length, that is , $d = 100m$ .
As we know that speed is given as distance travelled per unit time .
Mathematically, we can write ,
$v = \dfrac{d}{t}$
Where ,
‘v’ is the speed in meters per second ,
‘d’ is the distance travelled by train in meters ,
And ‘t’ is the time taken by train to cover the distance in seconds .
We get ,
$t = \dfrac{d}{v}$
Both the distance and speed should be in their corresponding standard unit.
We have distance already in its standard unit.
Now, we are converting speed into its standard unit ,
$v = 30km/hr = \dfrac{{30 \times 1000}}{{60 \times 60}}m/\sec$
$= \dfrac{{50}}{6}m/\sec ................(2)$
Now, substitute $(1),(2)$ in $t = \dfrac{d}{v}$ ,
We will get the following,
$t = \dfrac{d}{v} = \dfrac{{100}}{{\dfrac{{50}}{6}}}$ sec
Simply the above expression, we will get ,
$t = \dfrac{{100 \times 6}}{{50}}$ sec
Simply the above expression, we will get ,
$\therefore t = 12\sec$
Therefore, we can say that option ‘C’ is the correct option.

Note :
In the given question, no mathematical formula except the relation $1km = 1000m$ and $v = \dfrac{d}{t}$
Where ,
‘v’ is the speed in meters per second ,
‘d’ is the distance travelled by train in meters ,
And ‘t’ is the time taken by train to cover the distance in seconds .
is being used only the mathematical operations such as addition, subtraction, multiplication and division is used. Questions similar in nature as that of above can be approached in a similar manner and we can solve it easily.