A train with 90 km/hr crosses a bridge in 36 seconds. Another train 100 meters shorter crosses the same bridge at 45 km/hr. What is the time taken by the second train to cross the bridge?

Answer: Option D

Let the lengths of the train and the bridge be x meters and y meters respectively.
Speed of the first train
= 90 km/hr
= $$\left(90\times \frac{5}{18}\right)$$  m/sec
= 25 m/sec
Speed of the second train = 45 km/hr
= $$\left(45\times \frac{5}{18}\right)$$  m/sec
= $$\frac{25}{2}$$ m/sec
Then, $$\frac{\text{x}+\text{y}}{36}$$ = 25
⇒ x + y = 900
∴ Required time
$$\begin{array}{rl}& =\left[\frac{\left(\text{x}-100\right)+\text{y}}{\frac{25}{2}}\right]\text{sec}\\ & =\left[\frac{\left(\text{x}+\text{y}\right)-100}{\frac{25}{2}}\right]\text{sec}\\ & =\left(800\times \frac{2}{25}\right)\text{sec}\\ & =64\text{sec}\end{array}$$