Multiple choice

A person borrows a certain amount of money at 5% simple interest and he lends that amount to another person at 10% compound interest, after three years his profit is Rs.905. Find out the amount he borrowed.

  1. Rs. 2000

  2. Rs. 3000

  3. Rs. 5000

  4. Rs. 8000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal. Simple interest after 3 years is 0.05 * 3 * P = 0.15P. Compound interest after 3 years is P * (1.10^3 - 1) = P * (1.331 - 1) = 0.331P. Profit = 0.331P - 0.15P = 0.181P = 905. P = 905 / 0.181 = 5000.

AI explanation

Let the borrowed principal be P, so the simple interest to be paid over 3 years at 5% is (P * 5 * 3)/100 = 0.15P. The compound interest received from lending at 10% for 3 years is P(1 + 10/100)^3 - P, which simplifies to P(1.331 - 1) = 0.331P. His profit is the difference between the interest received and paid, so 0.331P - 0.15P = 905, meaning 0.181P = 905, and therefore P = Rs. 5000.

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