Question 100

# 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?

Solution

Let us assume that the length of each bogy is 1 unit, and the speed of both A and B be s units.

Initially, both A and B had 12 bogies, and ran in opposite direction.

So, using the concept of relative speed, the effective speed of the two trains taken together, when travelling in opposite direction adds up.

Effective distance covered = 12+12 units=24.

Effective speed= 2s units.

Now, using time=Â $$\ \frac{\ Dis\tan ce}{Speed}$$, we get 2 mins=Â $$\ \frac{\ 24}{2s}$$

=>120=$$\ \frac{\ 12}{s}$$

.'.s=Â $$\ \frac{\ 1}{10}$$

In the new scenario, length of B becomes 16 units.

So,Â Effective distance covered = 12+16 units=28 units.

Effective speed= 2s units.

New time=Â $$\ \frac{\ 28}{2s}=\ \frac{\ 14}{s}$$=140.

So, increase in time in the new case= 140-120 seconds= 20 Seconds- Option D.

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