Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

To solve this problem, we first need to understand that the speed of the train is constant, and when it crosses a person or an object, it covers the length of itself.

1. Let's denote the speed of the train as 'x' km/hr and its length as 'L' km.

2. When the train crosses the first person (who is walking at 2 km/hr), it covers the distance of its own length 'L' at a relative speed of (x-2) km/hr in 90 seconds. We can write this as: L = (x-2) * (90/3600) ---- (equation 1) (We divide by 3600 to convert the time from seconds to hours as the speed is given in km/hr)

3. Similarly, when the train crosses the second person (who is walking at 4 km/hr), it covers the distance of its own length 'L' at a relative speed of (x-4) km/hr in 100 seconds. We can write this as: L = (x-4) * (100/3600) ---- (equation 2)

4. Now we have two equations with two variables, which we can solve simultaneously to find the values of 'x' and 'L'.

5. By equating equation 1 and equation 2, we get: (x-2) * (90/3600) = (x-4) * (100/3600) Solving this equation gives us the value of 'x' (the speed of the train) as approximately 72 km/hr.

6. Substituting 'x' in equation 1, we get the length 'L' of the train as approximately 1.5 km.

7. Now, the time taken by the train to cross an electric post would be the time it takes to cover a distance equal to its own length at its own speed. So, we can calculate this as: Time = L / x * 3600 = 1.5 / 72 * 3600 = approximately 75 seconds.

So, the train would take approximately 75 seconds to cross an electric post.