CAT 2023 Interest — Previous Year Question

Jose borrowed some money from his friend at simple interest rate of $10\%$ and invested the entire amount in stocks. At the end of the first year, he repaid $\tfrac{1}{5}$ of the principal amount. At the end of the second year, he repaid half of the remaining principal amount. At the end of third year, he repaid the entire remaining principal amount. At the end of the fourth year, he paid the last three years’ interest amount. As there was no principal amount left, his friend did not charge any interest in the fourth year. At the end of fourth year, he sold out all his stocks. Later, he calculated that he gained Rs. $97500$ after paying principal and interest amounts to his friend. If his invested amount in the stocks became double at the end of the fourth year, how much money did he borrow from his friend?