Well, here is my shot at your story. I split it up into separate sentences to make it easier to work on. My comments and suggestions are in square brackets under each of your original sentences.
I boarded a train from Mumbai heading towards Pune.
[Strictly speaking "a" is correct here but it is far more common for native speakers to say "I boarded
the train..."]
I got the companions in the group of businessmen sitting next to me.
[I found myself sitting next to a group of businessmen.]
They were discussing the future of politics in the country, debating about the results of forthcoming general elections.
[They were discussing the future of politics in the country, debating what the results of the forthcoming general election might be.]
One said, the congress will grab the large chuck of middle class votes as they presented the populist budget this financial year won everyone’s heart.
[One said the congress will grab a large chuck of the middle class vote, as they presented a populist budget this fiscal year and won everyone's heart.]
Other men instantly shot the words like rocket, he was of opine that all this is just a perception, that Government serious thinks about the middle class and poor of the country.
[Another man strongly disagreed, he was of opinion that all this is wrong, that the Government seriously thinks about the middle class and the poor of the country.]
Progress in only restricted to urban, so many farmers are committing suicides everyday, millions are still below poverty line, millions still go to bed without eating, millions struggle with their lives living with $2 per day.
[It's not clear here who is expressing this opinion. Is it one of the businessmen or is it the author of the story or someone else? You need to clarify this. By the way, the repetition of the word millions here is a good touch. It really emphasizes the number of people in distress.
Progress is restricted to urban areas, many farmers are committing suicide every day, millions are living below the poverty line, millions go to bed without eating, millions struggle to live on $2 per day.]
Other person nodded agreeing to his views.
[Some of the others nodded in agreement.]
By the rime train chugs at the station, I really liked their conversations how time passed me I didn’t released, I reached my destiny, I disembarked from the train thinking they were politicians or businessmen
[Even though "rime" is technically correct here it is an extremely uncommon word--I'm a native speaker of English and I had to look it up. I would recommend not using it or providing some context to justify its use.
I was so interested in their conversation that I was surprised when the [rime?] train chugged into the station. I hadn't released the time was passing so quickly. Having reached my destination, I disembarked from the train wondering if they were politicians or businessmen.]