Two trains are moving in opposite directions at 60km/h and 90km/h. Their lengths are 1.2 km and 0.8 km respectively. In how much time will they cross each other?

Correct option is C

Given
Speed of first train $$(S_1)$$​= 60 km/h
Speed of second train $$(S_2)$$​ = 90 km/h
Length of first train $$(L_1$$​) = 1.2 km = 1200 m
Length of second train ($$L_2)$$​ = 0.8 km = 800 m

Formula Used
Relative Speed (opposite directions) = $$S_1 + S_2$$​​
Time to cross = $$\frac{\text{Total Distance (Lengths)}}{\text{Relative Speed}}$$​​
Conversion: 1 km/h = $$\frac{5}{18} m/s$$​​
Solution
Relative Speed = 60 + 90 = 150 km/h
Speed in m/s =  $$150 \times \frac{5}{18} = \frac{750}{18} = \frac{125}{3} m/s$$​​
Calculate total distance to be covered to cross each other:
Total Distance = 1200 + 800 = 2000 m
 $$Time = \frac{2000}{\frac{125}{3}} \\\ \\Time = 2000 \times \frac{3}{125} \\\ \\Time = 16 \times 3 = 48 seconds$$​​
Final Answer
So the correct answer is (c)