m/s to km/hr conversion.

Speed of the faster train = $$\frac{160}{12}=\frac{40}{3}\ $$ m/s

Speed of the slower train = $$\frac{40}{3}-\left(6\times\ \frac{5}{18}\right)=\frac{35}{3}$$ m/s

Sum of speeds (when the trains travel towards each other) = $$\frac{40}{3}+\frac{35}{3}=25$$ m/s

Let the slower train be $$x$$ metres long; then: $$\frac{160+x}{25}=14$$

On solving, $$x=190\ m$$

It is given that the speed of Ravi is 40 kmph, which is equal to $$\frac{100}{9}$$ m/s. It is also known that the speed of Ashok is 50 kmph, which is equal to $$\frac{125}{9}$$ m/s.

It is known that the distance between Ravi and Ashok is 225 meters, and the relative speed of Ravi and Ashok is $$\frac{125}{9}+\frac{100}{9}=25$$ m/s 

Hence, they will meet each other in $$\frac{225}{25}=9$$ seconds. The distance traveled by Ravi in these 9 seconds is $$\frac{100}{9}\times\ 9=100$$ meters.

Since Vijay was already 54 meters behind Ravi when they were starting, Vijay must travel (100+54) = 154 meters in these 9 seconds.

Hence, the speed of Vijay is $$\frac{154}{9}$$ m/s, which is equal to $$\frac{154}{9}\times\ \frac{18}{5}\ =\frac{308}{5}=61.6$$ kmph.

The correct option is C

The speeds in m/s are 36/(18/5) =10m/s and 45/(18/5)=12.5m/s. Ram completes a circle in 100 seconds, while Shyam completes a circle in 80 seconds. So, minimum time is LCM(80,100) = 400 seconds