Subject: General Aptitude · Chapter: Problems on Trains · Exam: 2007 · Marks: · Difficulty:
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
Answer
Answer (as printed): A
Explanation
Let the length of each train be $x$ metres and let the speed of each of them by $y \mathrm{m} / \mathrm{sec}$. $$\text { Then, } \frac{2 x}{2 y}=120 \Leftrightarrow \frac{x}{y}=120$$ New length of train $A=\left(\frac{16}{12} x\right) \mathrm{m}=\left(\frac{4 x}{3}\right) \mathrm{m}$. ∴ Time taken by trains to cross each other $$=\left(\frac{x+\frac{4 x}{3}}{2 y}\right) \sec =\frac{7 x}{6 y}=\frac{7}{6} \times \frac{x}{y}=\left(\frac{7}{6} \times 120\right) \sec =140 \sec .$$ Hence, difference in times taken $$=(140-120) \mathrm{sec}=20 \mathrm{sec} .$$