A train with 90 kmph crosses a bridge in 36 s. Another train 100 m shorter crosses the same bridge at 45 kmph. The time taken by the second train to cross the bridge will be

Let the length of first train be $$Y$$ metres & length of bridge be "X" metres.
So, now the length of second train will be = (Y-100) metres.

First train speed = $$\dfrac{\ 450}{18}$$ = 25 m/s

Second train speed = $$\dfrac{\ 225}{18}$$ = 12.5 m/s

Time taken by first train = $$\dfrac{\ Y\ +X}{25}=36$$

It implies, (Y+X) = 25(36).

Time taken by Second train = $$\dfrac{\ Y\ +X-100}{12.5}$$ = $$\dfrac{25\left(36\right)-100}{12.5}$$ = 64 seconds