​Let Chennai and Trivandrum be two stations 690 km apart. A train starts from Chennai at 8:00 p.m. and travels towards Trivandrum at a speed of 75 km/h. Another train starts from Trivandrum at 9:00 p.m. and travels towards Chennai on the parallel track at a speed of 60 km/h. At what time will they meet?

Correct option is D

Given:

Distance between the stations = 690 km.

Speed of the train starting from Chennai (1$$^{st}$$​ train), S$$_1$$​ = 75 km/h.

Speed of the train starting from Trivandrum (2$$^{nd}$$​ train) S$$_2$$​ = 60 km/h.

Train from Chennai starts at 8:00 p.m.

Train from Trivandrum starts at 9:00 p.m.

Formula used :

Speed = $$\frac{Distance }{Time}$$​​

When both trains start traveling towards each other ,

Relative speed = $$S_1 +S_2$$​ 

Solution:

Distance covered by the first train before 9:00 p.m.

Distance covered by first train in 1 hour = 75km.

So, at 9:00 p.m., the distance between the two trains is:

690 − 75=615 km

Relative speed of the two trains :

75 + 60 = 135km/h.

​$$\text{Time to meet} = \frac{\text{Distance}}{\text{Relative speed}}= \frac{615}{135} = \frac{41}{9}\, \text{hours}.$$

 4.56 $$\frac{41}{9}\text{hours} = 4 \, \text{hours} \ 33\ \text{minutes} \ 20 \, \text{sec}$$

​The trains start traveling towards each other at 9:00 p.m. :

9:00 p.m. + 4 hours, 33 minutes and 20 sec = 1:33 :20 a.m. (next day)

The correct answer is 1:33 :20 a.m.​​