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1. A man standing on a platform finds that a train takes 3 seconds to pass him and another train of the same length moving in the opposite direction takes 4 seconds. The time taken by the trains to pass each other will be :

A. $2 \frac{3}{7}$ seconds

B. $3 \frac{3}{7}$ seconds

C. $4 \frac{3}{7}$ seconds

D. $5 \frac{3}{7}$ seconds

Solution:

Let the length of each train be x meters
Then, speed of first train =

\frac{x}{3}

m/sec
Speed of second train =

\frac{x}{4}

m/sec
∴ Required time

\begin{aligned} = [\frac{x + x}{(\frac{x}{3} + \frac{x}{4})}] sec \\ = [\frac{2 x}{(\frac{7 x}{12})}] sec \\ = (2 \times \frac{12}{7}) sec \\ = \frac{24}{7} sec \\ = 3 \frac{3}{7} sec \end{aligned}

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