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?

Answer: Option A

Let the length of each train be x meters and let the speed of each of them by y m/sec
Then, $$\frac{\text{2x}}{2\text{y}}$$ = 120
⇒ $$\frac{\text{x}}{\text{y}}$$ = 120 . . . . . . . (i)
New length of train A $$=\left(\frac{16}{12}\text{x}\right)\text{m}=\left(\frac{4\text{x}}{3}\right)\text{m}$$
∴ Time taken by trains to cross each other
$$\begin{array}{rl}& =\left(\frac{\text{x}+\frac{4\text{x}}{3}}{2\text{y}}\right)\text{sec}\\ & =\frac{7\text{x}}{6\text{y}}\\ & =\frac{7}{6}\times \frac{\text{x}}{\text{y}}\\ & =\left(\frac{7}{6}\times 120\right)\text{sec}\\ & =140\text{sec}\end{array}$$
Hence, difference in times taken
= (140 - 120) sec
= 20 sec