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XAT 2023 — QA & DI Question 3

Simple InterestEasy

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? 

Answer & solution

  • A

    250000

  • B

    200000

  • C

    150000

  • 125000

  • E

    None of the above

Solution

Let total amount borrowed by Jose = Rs. 5x.

Principal paid back is x at the end of 1st year, 2x at the end of 2nd year and 2x at the end of 3rd year.

Total interest accumulated = x × 1 × 0.1 + 2x × 2 × 0.1 + 2x × 3 × 0.1 = 1.1x

∴ Total amount Jose needs to pay = 5x + 1.1x = 6.1x

Value of stocks doubled i.e., 10x

Now, Jose's profit = 97500
⇒ 97500 = 10x - 6.1x
⇒ 3.9x = 97500
⇒ x = 25,000

∴ Money borrowed by Jose = 5x = 1,25,000

Hence, option (d).

XAT 2023 QA & DI Q3: Jose borrowed some money from his friend at simple interest rate of 10% and invested the entire amount in stoc — Solution | TheCATExam