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 1/5th 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?
Let the amount Jose borrowed be 'x'. The rate of interest is 10%
Interest occurred on 'x' is = $$\ \frac{\ x\times1\times\ \ 0.1\ }{5}+\ \frac{\ 2x\ \times2\times\ \ 0.1}{5}\ +\ \ \frac{2x\times\ 3\times\ 0.1\ }{5}$$
= $$\ \frac{\ 1.1x\ }{5}$$
The invested amount doubled at the end of the fourth year, i.e. 2x.
Jose's profit after paying principal and interest amounts to his friend at the end of the fourth year is Rs 97500.
i.e., $$\ 2x-x-\frac{\ 1.1x\ }{5}=97500$$
$$\frac{\ 3.9x}{5}=97500$$
$$\ \ \ \ x=125000$$
The amount that Jose borrowed is Rs 1,25,000.
Option (D) is correct.
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