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1. Two identical trains A and B running in opposite directions at same speed take 2 minutes to cross each other completely. The number of bogies of A are increased from 12 to 16. How much more time would they now require to cross each other?

A. 20 sec

B. 40 sec

C. 50 sec

D. 60 sec

Solution:

Let the length of each train be x meters and let the speed of each of them by y m/sec
Then,

\frac{2x}{2 y}

= 120
⇒

\frac{x}{y}

= 120 . . . . . . . (i)
New length of train A

= (\frac{16}{12} x) m = (\frac{4 x}{3}) m

∴ Time taken by trains to cross each other

\begin{aligned} = (\frac{x + \frac{4 x}{3}}{2 y}) sec \\ = \frac{7 x}{6 y} \\ = \frac{7}{6} \times \frac{x}{y} \\ = (\frac{7}{6} \times 120) sec \\ = 140 sec \end{aligned}

Hence, difference in times taken
= (140 - 120) sec
= 20 sec

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