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 Concept.
Both trains always travel at the same fixed speed before and after the change, so the crossing time is directly proportional to the combined length of the two trains, since the combined speed never changes. This means the actual speed value is not even needed; a simple ratio does the job.

Step 2: Key Formula or Approach.
$\text{time} \propto \text{combined length}$, when combined speed stays constant. So:
\[ \frac{\text{new time}}{\text{old time}} = \frac{\text{new combined length}}{\text{old combined length}} \]

Step 3: Detailed Explanation.
Old combined length (in bogies) $= 12+12 = 24$.
New combined length $= 16+12 = 28$.
Old time $= 2$ minutes $= 120$ seconds.
Using the proportion:
\[ \text{new time} = 120\times\frac{28}{24} = 120\times\frac{7}{6} = 140 \text{ seconds} \]

Step 4: Final Answer.
Extra time required $= 140-120 = 20$ seconds, which is option (D).
\[ \boxed{20 \text{ seconds}} \]