Question

Two trains of equal length are running on the parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is?
A. 50 m
B. 80 m
C. 72 m
D. 82 m

Answer 1

Hint: Since, the trains are running in the same direction, so the relative speed of the trains is $46 - 36 = 10km/hr$, also the two trains are of equal length, so the total distance covered will be twice the length of each trains, use this concept to solve the question.

Complete step-by-step answer:
We have been given in the question-
Speed of one train is 46 km/hr.
Speed of another train is 36 km/hr.
Let us assume the length of each train is x meter.
So, the total distance = x + x = 2x.
Now we know, when two objects are moving in the same direction with speed x km/hr and y km/hr (assume) then the relative speed is $(x - y)km/hr$ .
Now, since the trains are also running in the same direction, so, the relative speed =$46 - 36 = 10km/hr$
Now, to convert km/hr to m/s we use the formula- $xkm/hr = x \times \dfrac{5}{{18}}m/s$.
Hence the relative speed in m/s will be $10km/hr = 10 \times \dfrac{5}{{18}} = \dfrac{{25}}{9}m/s$.
Now, we know that Distance = Speed * Time
Put distance = x, speed = 25/9 m/s, time = 36 seconds.
We get-
$D = S \times T \\\ \Rightarrow 2x = \dfrac{{25}}{9} \times 36 \\\ \Rightarrow 2x = 25 \times 4 = 100 \\\ \Rightarrow x = 50m \\\$
Hence, the length of each train is 50 m.
So, the correct option is A.

Note – Whenever such types of questions appear, then write down the values given in the question. Assume the length of each train to be x, so we can say the distance covered is x + x = 2x. Then find the relative speed, and then use the formula that Distance = Speed * Time, put all the values and find the value of x, which is the length of the train.