Question

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. 40s
• B. 50s
• C. 60s
• D. 20s

Answer 1

The Correct Option is D

To determine how much more time the trains require to cross each other, we follow these steps:

Step 1: Determine Original Time
The trains take 2 minutes to cross each other completely. Since time can be converted to seconds to ease calculations, we have:

Time_original = 2 minutes = 120 seconds.

Step 2: Calculate Effective Length:
Assume each bogie has a length L. Let the original effective length when both trains have 12 identical bogies be 24L (because there are two trains each with 12 bogies).

Step 3: Calculate Relative Speed
Let v be the speed of each train.
The relative speed when the trains move in opposite directions is given by
Sum of speeds = 2v.
Since they take 120 seconds to cross, we can express this as:
24L = 2v × 120, therefore
v = L/10.

Step 4: Determine New Effective Length
With the increased bogies in train A, A now has 16 bogies.
Hence, the new effective length when trains A and B have 16 and 12 bogies respectively is (16L + 12L) = 28L.

Step 5: Calculate New Time
Let the new crossing time be t seconds:
28L = 2v × t.
Substitute v = L/10 from Step 3:
28L = 2(L/10) × t,
Simplifying gives t = 140 seconds.

Step 6: Calculate Additional Time Required
Additional time = New time - Original time = 140 - 120 = 20 seconds.

Therefore, the trains would require 20 additional seconds to cross each other when train A has 16 bogies.

Answer: 20s