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 :

Solution (By Examveda Team)

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