Question

A train running at the speed of $60$ km/hr crosses a pole in $9$ seconds. What is the length of the train?
A.$150$ meters
B.$180$ meters
C.$324$ meters
D.Cannot be determined
E.None of these

Answer 1

Hint: First, we will convert the unit km/hr to m/sec because we have to obtain the answer in meters. We know that $1{\text{ Km = 1000m}}$ and $1{\text{ hr = 3600sec}}$. So use these values to change the unit. Then use the formula of Distance which is given as- Distance =speed ×time
Put the given values in the formula and solve it to get the answer. The distance travelled by train in crossing the pole is the length of the train.

Complete step-by-step answer:
Given, the speed of the train =$60$km/hr
We know that $1{\text{ Km = 1000m}}$ and $1{\text{ hr = 60min}}$ and $1\min = 60{\text{ sec}}$ so $1{\text{ hr = 60}} \times {\text{60 = 3600sec}}$
So $60$km/hr=$60 \times \dfrac{{1000}}{{3600}}$ m/sec
On solving, we get-
$ \Rightarrow 60$ Km/hr=$\dfrac{{100}}{6} = \dfrac{{50}}{3}$ m/sec
The time it takes the train to cross a pole=$9$ seconds
We have to find the length of the train.
Here, the distance covered by the train to cross the pole will be the length of the train.
We know that the formula of distance is given as-
$ \Rightarrow $ Distance =speed ×time
On putting the values in the formula, we get-
$ \Rightarrow $ Distance=$\dfrac{{50}}{3} \times 9$ m
On solving, we get-
$ \Rightarrow $ Distance=$50 \times 3$ m
Om multiplication, we get-
$ \Rightarrow $ Distance=$150$ m
So since distance= length of the train
The length of the train=$150$ m
The correct answer is option A.

Note: When we change the unit from km/hr to m/sec we simply multiply the value by $\dfrac{5}{{18}}$ because we know that $1{\text{ Km = 1000m}}$ and $1{\text{ hr = 3600sec}}$ but if we have to convert meter per second to km per hour then we will multiply $\dfrac{{18}}{5}$ to the value to change the unit.