Question

Jose borrowed some money from his friend at a 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?

• A. 250000
• B. 200000
• C. 150000
• D. 125000
• E. None of the above

Answer 1

The Correct Option is D

Let the amount Jose borrowed be P. The simple interest (SI) for one year is calculated as follows:

SI = P × 10% = 0.1P

The events occur as follows:

1. At the end of the first year, Jose repaid 1/5th of the principal amount:
   Remaining principal = P - (P/5) = 4P/5
   The interest for the first year is: 0.1P
2. At the end of the second year, Jose repaid half of the remaining principal amount:
   Remaining principal = 4P/5 - (1/2)×(4P/5) = 2P/5
   The interest for the second year is: 0.1 × (4P/5) = 0.08P
3. At the end of the third year, Jose repaid the entire remaining principal:
   Remaining principal = 2P/5 - 2P/5 = 0
   The interest for the third year is: 0.1 × (2P/5) = 0.04P
4. At the end of the fourth year, Jose paid the last three years’ interest amount:
   Total interest paid ={0.1P + 0.08P + 0.04P} = 0.22P
   Since Jose sold his stocks for double the amount he invested:
   Investment = P
   Stock value = 2P
   Jose's net gain after paying principal and interest:
   (2P) - (P) - (0.22P) = P - 0.22P = 0.78P
   Given that Jose gained Rs. 97500:
   0.78P = 97500

P = 97500 / 0.78

P = 125000

Thus, the amount Jose borrowed from his friend is Rs. 125000.