Train crosses a bridge which is 250 m long in 25 sec. Find the time taken by train to cross a man running in opposite direction at speed of 15m/sec. Find the speed of train.

The correct option is Can’t be determined.

To understand why the speed of the train and the time taken to cross the man cannot be calculated, let us set up the mathematical equations based on the given information.

Let:
- $L$ be the length of the train in meters.
- $v$ be the speed of the train in meters per second (m/sec).

Step 1: Analyze the train crossing the bridge
When a train crosses a bridge, the total distance covered is the sum of the length of the train and the length of the bridge (250 m).
Using the formula:

$\mathrm{Distance}=\mathrm{Speed}\times \mathrm{Time}$

We can substitute the given values:

$L+250=v\times 25$

$L+250=25v$

This gives us a single linear equation with two independent variables: length of the train ($L$) and speed of the train ($v$). There are infinitely many pairs of ($L$, $v$) that satisfy this single equation.

Step 2: Analyze the train crossing the man
When the train crosses a man running in the opposite direction at 15 m/sec, the relative speed of the train with respect to the man is $v+15$ m/sec.
The distance to be covered to cross the man is simply the length of the train ($L$).
The time $t$ taken to cross the man would be given by:

$t=\frac{L}{v+15}$

Conclusion:
Since we have two unknown quantities ($L$ and $v$) but only one relationship connecting them ($L+250=25v$), we cannot uniquely calculate either the speed of the train ($v$) or its length ($L$). Consequently, the time $t$ taken to cross the man also cannot be calculated.

Thus, the correct answer is Can’t be determined.