# A train travelling at 50kmph crosses another train travelling in the same direction at 32 kmph in 45 seconds. Find the time taken(in seconds) to cross

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A train travelling at 50kmph crosses another train travelling in the same direction at 32 kmph in 45 seconds. Find the time taken(in seconds) to cross when both the trains travel in the opposite direction?
1. 405/41
2. 407/51
3. 415/31
4. 413/41

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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