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?

Solution(By Examveda Team)

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
$$\eqalign{ & = \left[ {\frac{{\left( {{\text{x}} - 100} \right) + {\text{y}}}}{{\frac{{25}}{2}}}} \right]{\text{sec}} \cr & = \left[ {\frac{{\left( {{\text{x}} + {\text{y}}} \right) - 100}}{{\frac{{25}}{2}}}} \right]{\text{sec}} \cr & = \left( {800 \times \frac{2}{{25}}} \right){\text{sec}} \cr & = 64\,{\text{sec}} \cr} $$