Question

A train 600 meters long is running at a speed of $90{\text{ km/hr}}$. If it crosses a tunnel in one minute, then the length of the tunnel is
A.500 meters
B.550 meters
C.600 meters
D.900 meters

Answer 1

Hint: In this question, we need to determine the length of the tunnel through which the train of length 600 meters must pass at the speed of $90{\text{ km/hr}}$ in the time period of 10 minutes. For this, we will use the relation between the distance, velocity and time which is given as $d = vt$.

Complete step-by-step answer:
The product of the velocity of the body with the time of travel results in the total distance travelled by the body. Mathematically, $d = vt$ where, ‘d’ is the distance travelled by the body, ‘v’ is the velocity of the train and ‘t’ is the total time taken by the body to travel that distance.
Here, total distance travelled by train to cross the tunnel is the summation of the length of the tunnel, and the length of the train itself as the body is said to be passed completely when its trail passed the particular point.
Let the length of the tunnel be $x$ meters.
So, the total distance to be travelled by train to pass the tunnel completely is given as $d = \left( {600 + x} \right){\text{ meters}}$.
Now, convert the velocity of the train which is given in ${\text{km/hr}}$ to ${\text{m/s}}$ as the length has been given in meters.
$
  90{\text{ km/hr}} = \dfrac{{90 \times 1000}}{{60 \times 60}}{\text{ m/s}} \\
  {\text{ = 25 m/s}} \\
 $
Also, convert the time which is given in minutes to seconds as the speed is in seconds as well.
$1{\text{ min}} = 60{\text{ sec}}$
Now, substitute $d = \left( {600 + x} \right){\text{ meters, }}v = 25{\text{ m/s and }}t = 60{\text{ sec}}$ in the formula $d = vt$ to determine the length of the tunnel.

$
 d = vt \\
 600 + x = 25 \times 60 \\
 x = 1500 - 600 \\
 = 900{\text{ meters}} \\
 $
Hence, the length of the tunnel is 900 meters.
So, the correct answer is “Option D”.

Note: Candidates should be careful while using the units in the formula. All the units should be converted in similar ones before substituting them in the formula.