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1. 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?

A. 61 seconds

B. 62 seconds

C. 63 seconds

D. 64 seconds

Solution:

Let the lengths of the train and the bridge be x meters and y meters respectively.
Speed of the first train
= 90 km/hr
=

(90 \times \frac{5}{18})

m/sec
= 25 m/sec
Speed of the second train= 45 km/hr
=

(45 \times \frac{5}{18})

m/sec
=

\frac{25}{2}

m/sec
Then,

\frac{x + y}{36}

= 25
⇒ x + y = 900
∴ Required time

\begin{aligned} = [\frac{(x - 100) + y}{\frac{25}{2}}] sec \\ = [\frac{(x + y) - 100}{\frac{25}{2}}] sec \\ = (800 \times \frac{2}{25}) sec \\ = 64 sec \end{aligned}

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