Two trains 150 m and 120 m long respectively moving from opposite direction cross each other in 10 sec. If the speed of the second train is 43.2 km/hr, then the speed of the first train is :

Answer: Option A

Let the speed of second train = x km/hr
Their relative speed in opposite direction :
= (43.2 + x) km/hr
According to the question,
$$\begin{array}{rl}& \text{Time = }\frac{l_1+l_2}{\text{Speed}}\\ & \Rightarrow 10\sec =\frac{\left(150+120\right)\text{m}}{\left(43.2+x\right)\times \frac{5}{18}\text{ m/s}}\\ & \Rightarrow 10\sec =\frac{270\times 18}{\left(43.2+x\right)\times 5}\\ & \Rightarrow 43.2\times 5+5x=486\\ & \Rightarrow x=\frac{486-216}{5}\\ & \Rightarrow x=54\end{array}$$
∴ Speed of the second train = 54 km/hr