Theory:

     “Yes, I am going to school,” I said, and stood up respectfully; she seemed poor, but there was a dignity about her that commanded respect.
 
     'I have been watching you for some time,’ she said 'Didn't your parents come to see you off ,'
 
     'I don't live here'; I said. 'I had to change trains. Anyway, I can travel alone.'
 
     'I am sure you can.’ she said, and I liked her for saying that and I also liked her for the simplicity of her dress and for her deep soft voice and the serenity of her face.
Explanation:
 
The woman had been watching the boy for a long time. So she approached him. After seeing the woman, the boy stood up with respect and answered that he was going to school after his vacation. Her appearance gave the impression of a poor woman, but he had great respect for her while speaking with her. Her simplicity and kindness made him talk to her.
 
Later on, the woman asked him, 'Didn't your parents come to see you off ?'. On hearing that, the boy started to tell her that he does not belong to this place. He had started his journey from home by bus and then he reached the railway station. Finally, he has to travel in different trains to get to his school, and also he expressed to her, 'I can travel alone.'

After listening to the boy, the woman said she was very sure that he could travel alone. The boy was impressed by her positive way of talking. The boy liked her simplicity in dressing, her gentle voice, and calmness on her face.
 
Meanings of the difficult words:
 
S.No
Words
Meanings
1
Dignity The state or quality of being worthy of honour or respect
2
Serenity The state of being calm, peaceful, and untroubled
3
Simplicity The quality of being simple or condition of being easy to understand
Reference:
State Council of Educational Research and Training (2019). Term-3 English Standard-8. The Woman on Platform 8 - Ruskin Bond (pp. 107-114). Published by the Tamil Nadu Textbook and Educational Services Corporation.