Theory:

     After about half-an-hour we left the dining-room and began walking back along the platform. An engine was shunting up and down beside platform No.8 and as it approached, a boy leapt off the platform and ran across the rails, taking a short cut to the next platform. He was at a safe distance from the engine, and there was no danger unless he had fallen; but as he leapt across the rails, the woman clutched my arm. Her fingers dug into my flesh, and I winced with pain. I caught her fingers and looked up at her, and I saw a spasm of pain and fear and sadness pass across her face. She watched the boy as he climbed other platform, and it was not until he had disappeared in the crowd that she relaxed her hold on my arm. She smiled at me reassuringly, and took my hand again: but her fingers trembled against mine.
 
     'He was all right.' I said, feeling that it was she who needed reassurance.
 
     She smiled gratefully at me and pressed my hand. We walked together in silence until we reached the place where I had left my suitcase, one of my school fellows, Satish, a boy of about my age, had turned up with his mother.
Explanation:
 
After having snacks for about half-an-hour at the dining-room, the woman and Arun left the place. They began to return to the old place where Arun had previously sat (platform no 8). They heard an engine sound while walking on the platform (a train was approaching the nearby platform).
 
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A train approached the nearby platform
 
When the train came beside platform no 8, a boy jumped off from the platform, ran across the rails and took the shortcuts to reach the next platform. The boy was on the safer side, and also, he was far away from the engine. No danger would come his way if he stood properly and did not fall.

When the boy jumped across the rails, the woman grabbed Arun's hand tightly in fear. While she held his hand, unknowingly, her hands dug into his flesh. Arun felt hurt and pain in his hands. Due to extreme pain, Arun caught her fingers immediately and looked up at her. Arun noticed the emotions of fear, pain, and sadness on her face.
 
The woman was worried about the boy who jumped over the rails to reach the next platform. She kept an eye on the boy as he climbed to the next platform, and she didn't let go of Arun's arm until the boy was lost in the crowd. But Arun caught her sight, and he understood what was going through her mind and said, 'He was all right.' The woman smiled at Arun after hearing his words. She pressed his hands in the sense of everything was alright. Nothing had gone wrong.
 
Later on, Arun and the woman started to walk again. They walked together in silence until they reached the place where Arun kept his suitcases. While they went there, Arun noticed one of his school friends named Satish, nearly the same age as Arun (probably twelve-year-old). Satish came to the railway station along with his mother.
 
Meanings of the difficult words:
 
S.No
Words
Meanings
1
Trembled The hands started to shiver typically as a result of anxiety, excitement, or frailty
2
Disappeared Be lost or go missing; become impossible to find
3
ReassuranceThe action of removing someone's doubt or fear
4
Clutched Grasp something tightly
5
Spasm A sudden involuntary muscular contraction or convulsive movement
6
Shunting Pushing or pulling a train or part of a train from one line of rails to another
7
Leapt Jump or spring a long way, to a great height, or with great force
8
Winced
Make a slight shrinking movement of the body out of pain or distress
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.