Theory:

     And he ordered a new stake to be made ready for the execution. As the servants sharpened the stake and got it ready for the final impaling of the criminal, it occurred to the minister that the rich merchant was somehow too thin to be properly executed on the stake. He appealed to the king’s common sense. The king too worried about it.

     “What shall we do?” he said, when suddenly it struck him that all they needed to do was to find a man fat enough to fit the stake. The servants were immediately sent all over the town looking for a man who would fit the stake, and their eyes fell on the disciple who had fattened himself for months on bananas and rice and wheat and ghee.
Explanation:
 
When the king concluded that the merchant was the actual criminal, he ordered his servants to prepare a new stake for the merchant's execution. A stake is a sharp, pointed post that is used to penetrate through something.
 
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A wooden stake
 
The servants sharpened the stake after hearing their majesty's command. Finally, they prepared the stake and kept it ready for the final impaling of the culprit. When the new weapon was getting ready, the minister felt that the merchant was very thin and could not be executed on the stake. When he told the king about it, the king became more worried.
 
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Impaling (A type of punishment given for the offenders)
 
After listening to the minister's point, the king asked, "What shall we do?" Then the king got an idea right away that they should find a man who was fat enough to be executed on the stake. The merchant would not be executed because he was too thin. They thought of punishing another person instead of the merchant - one who was fat enough to be executed. Finally, the king sent his servants around the kingdom to look for a fat man to be executed on the stake. They found the guru's disciple, who had fattened because of overeating.
 
Meanings of the difficult words:
S.No
Words
Meanings
1
Stake A sharp, pointed post that is used to penetrate through something
2
Sharpen To make something sharp or sharper
3
Impaling To push a sharp object through something, especially the body of an animal or person
4
Appeal To make a serious or formal request, especially to the public, for money, information, or help
Reference:
National Council of Educational Research and Training (2006). Moments. In the Kingdom of Fools– A K Ramanujan (pp. 19-24). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.