Question

A train 800 meters long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minutes, then the length of the tunnel (in meters) is:
(a) 130
(b) 360
(c) 500
(d) 540

Answer 1

Hint: Let the length of the tunnel be x meters. So, the distance travelled by tunnel is given by (x+800) meters, because the length of the train is added to the distance. Then use the formula $\text{distance=speed }\!\!\times\!\!\text{ time}$ , and substitute the values given in the question and equate it with (x+80) to get the answer.

Complete step-by-step answer:
Let us start the solution to the above question by letting the length of the tunnel be x meters. So, the distance travelled by tunnel is given by (x+800) meters, because the length of the train is added to the distance. The length of train is added because the timer was started as soon as the engine entered the tunnel but it was stopped when the last cart of the train left the tunnel, by the time the timer was stopped the engine was 800 meters away from the end of the tunnel.
Also, we know that $\text{distance=speed }\!\!\times\!\!\text{ time}$ , so the distance travelled in 1 minute, i.e., $\dfrac{1}{60}hrs$ is :
$\text{distance=78 }\!\!\times\!\!\text{ }\dfrac{1}{60}$
Also, distance is equal to (x+800) meters which is equal to $\dfrac{x+800}{1000}\text{ km}$ .
$\dfrac{x+800}{1000}=78\times \dfrac{1}{60}$
$\Rightarrow x+800=1300$
$\Rightarrow x=500\text{ meters}$
So, the length of the tunnel is 500 meters.

Note: Remember that the length of the train must be added to the distance travelled to get the correct result. However, if the length of the train is not mentioned in any manner in the question, then you have to consider the train as a point object and solve the question accordingly. Also, be very careful about the units, as in the above question the units of elements are very random. You should know that 1 km=1000 meters and 1 hour is equal to 60 minutes.