A 180 meters long train crosses another train having length 270 m in 54/5 seconds by running towards each other. If the ratio of speed of the first train to second train is 2 : 3, then find the time taken by 2nd train to cross first train if both running in the same direction?

Correct option is C

Information given:
A 180 meters long train crosses another train having length 270 m in 54/5 seconds by running towards each other
The ratio of speed of the first train to second train is 2 : 3
Formulas Used:
Distance (when two train running towards each other) = length of first train + length of second train
Speed = Distance/time
Time = Distance/speed
Explanation:
Let speed of first and second train in m/second be 2x and 3x respectively.
Sum of the length of first train and second train ⇒ 180 + 270 = 450 m
Sum of their speeds =
2x + 3x = (450×5)/54
5x=125/3 m/s
x=25/3 m/s
Time taken by second train to cross first train =450/(3x-2x)=450/25×3=54 seconds