Correct Answer - Option 1 : 405/41

Given:

A train travelling at 50kmph crosses another train travelling in the same direction at 32 kmph in 45 seconds.

Formula:

If the lengths of two trains are a and b,

Time taken to cross each other when travelling in same direction = (a + b)/(va - vb)

Time taken to cross each other when travelling in opposite direction = (a + b)/(va + vb)

where va and vb are the speeds of trains A and B respectively.

Calculation:

Let the lengths of the trains be L1 and L2 respectively.

Relative speed = 18kmph = 5m/s

(L1 + L2) = 5(45) = 225

Relative speed when both the trains travel in opposite direction = (50 + 32) = 82 kmph = 205/9 m/s

The time taken to cross when both the trains travel in the opposite direction =

(L1 + L2)/(205/9) = 225(9)/205 = 405/41 seconds