Theory:

     "You looked such a sight on top of that cow," he said and started laughing.
 
     Then  he probably realised that I might have been hurt and asked, "Are you all right?"
     "Of course, I am," I said haughtily and got up at once.
 
     Nothing on earth would have made me admit to him how frightened and shaken I was. Just then my brother spotted one of the horse riders coming towards us with a thunderous scowl on his face. Behind him was the man to whom, in all probability, the cow belonged.
 
    My brother gave them an uneasy glance and said, " I think it would be nice if we moved quickly from here.”
 
    I looked round and saw that if both of us did not move fast enough, we would be called in for a lot of explanations. With one accord we got onto our bikes and beat a hasty retreat. The morning had already been rather eventful and we did not want to add another unpleasant episode to it.
Explanation:
 
The author's brother, being the one who had started the race, which led to the commotion, had been watching everything from a distance. He had seen the hilarious incident of the author clinging to the cow, her falling into the ditch and the man's pants getting torn. As her brother, he takes this chance to tease her. He teasingly says that it was so nice to see her sitting on top of the cow. He is not able to control his laughter as he is reminded of the incident. But since the relationship between sibling is not just about teasing and poking fun, his brotherly instincts show up. He cares for her as he is reminded of the fact that, she could be hurt from the whole incident as she had been carried across by a cow and thrown at the side of a ditch. He caringly enquires if she was alright, to confirm that the incident had not hurt her in any way showing that although siblings fight amongst themselves, they would be there for each other at a time of crisis.
 
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The brother tows the cycle with a smile
 
Siblings can also have ego issues. The author is visibly shaken by the incident and there is a chance that she might be hurt. But she does not let her brother know about it. She feels that it would be embarrassing to let him know the truth. She does not want to reveal that she has lost in the race as well. It is very general for people to act as though they are strong, when they face a problem. The author also does the same thing. She says that nothing on earth would make her accept that she was frightened and shaken from the incident. As they are having this conversation, her brother spots one of the horse riders who was part of the commotion, heading towards them. The riders were cavalry officers and they would also have the same feeling of being embarrassed in front of everyone, by falling down, not being able to control the horses, and getting pants torn. They do not like the fact that people could see their emotional and weaker side. Since it was caused by the author and her actions, they are angry with her. The officer walks towards them with an angry face. Followed by him is another angry face, which is that of the owner of the cow. He must also be upset because his cow had fallen into the ditch and was chased across the roads. The cow had done nothing but stood in a corner. He was also walking towards them, probably to demand an explanation.
 
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The officer is angry with her
 
The author's brother again becomes protective, as he knows that they had caused trouble and will be questioned for it. He does not want any harm on both of them. He therefore suggests that they leave immediately from the place, in order to escape further embarrassments. The author does not argue with her brother in this case, as she realizes that he is right. She realizes that if she does not move immediately along with her brother, she would be required to explain the situation to all of them. The brother and sister finally agreed upon one thing, that they had to leave. They did not wait for further orders. They took their bike and rode back home. The excitement that had prevailed in the morning had drained out of them. They had got a handful from the morning events and did not choose to ruin their day by the questioning.
 
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The brother leads his sister back home
 
Words with difficult meaning:
 
S.No
Words
Meaning
1
SightSomething that is seen
2
ThunderousA loud noise or an angry expression
3
ScowlAn angry look
4
ProbabilityChances that something might happen
5
GlanceA quick look
6
HastyFast
7
RetreatTo move or go back
8
EventfulExciting things happening continuously
Reference:
State Council of Educational Research and Training (2019). Term-3 English Standard-6. That Sunday Morning (pp 91-105). Published by the Tamil Nadu Textbook and Educational Services Corporation.