Question

Two identical trains A and B running in opposite directions at the 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. 40 s
• B. 50 s
• C. 60 s
• D. 20 s

Hint:

Since speed stays the same, crossing time is proportional to the combined length (in bogies) of the two trains.

Answer 1

The Correct Option is D

Step 1: Understanding the Question.
Two identical trains A and B move toward each other at the same speed and take 2 minutes to fully cross each other when both have 12 bogies. Train A's bogies are increased to 16 while B stays at 12, and we need the extra time needed to cross now.

Step 2: Key Formula or Approach.
When two trains cross each other moving in opposite directions:
\[ \text{time} = \frac{\text{length of A}+\text{length of B}}{\text{speed of A}+\text{speed of B}} \]
Since the bogies are identical, treat each bogie as 1 unit of length, so a train with \(n\) bogies has length \(n\) units. Let each train's speed be \(s\) units per minute.

Step 3: Detailed Explanation.
Originally, both trains have 12 bogies, so combined length \(=12+12=24\) units, and combined speed \(=s+s=2s\).
\[ 2 = \frac{24}{2s} \Rightarrow 2s = 12 \Rightarrow s = 6 \text{ units/min} \]
After the change, train A has 16 bogies and B still has 12, so combined length \(=16+12=28\) units, while combined speed stays at \(2s=12\) units/min.
\[ \text{new time} = \frac{28}{12} = \frac{7}{3} \text{ min} \]
Converting to seconds: \(\dfrac{7}{3}\times60=140\) seconds. The original time was \(2\) min \(=120\) seconds.

Step 4: Final Answer.
Extra time needed \(=140-120=20\) seconds. Options (A) 40 s, (B) 50 s and (C) 60 s do not match this calculation.
\[ \boxed{20 \text{ seconds}} \]