Two trains of equal length, running at the speed of 60 km/h and 40 km/h, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite direction?

Correct option is B

Given:

Speed of first train = 60 km/h

Speed of second train = 40 km/h

Time taken to cross each other when running in the same direction = 50 seconds

Formula Used:

Relative speed (same direction) = Speed of Train 1 − Speed of Train 2

Relative speed (opposite direction) = Speed of Train 1 + Speed of Train 2

Time to cross = $$\frac{\text{Total Length}}{\text{Relative Speed}}$$​​

Solution:

Let the length of each train be d.

When trains are moving in the same direction:

Relative Speed = 60 - 40 = 20 km/h

Convert the speed to meters per second:

20 km/h = $$\frac{20 \times 1000}{3600} = \frac{100}{18}$$​ m/s

The total distance covered when the trains cross each other is the sum of their lengths, 2d
Time taken to cross each other is 50 seconds, so:

​$$50 = \frac{2d}{\frac{100}{18}}\\ \ \\ \implies 2d = \frac{2500}{9}$$​​

When trains are moving in opposite directions:

Relative Speed = 60 + 40 = 100 km/h

Convert the speed to meters per second:

100 km/h = $$\frac{100 \times 1000}{3600} = \frac{1000}{36}$$​ m/s

The total length to be covered is 2L = $$\frac{2500}{9}$$​​

Time taken to cross each other:

Time = $$\frac{\frac{2500}{9}}{\frac{1000}{36}}$$​ = 10 seconds