Multiple choice

A man borrows money at 6% per annum, interest payable yearly, and lends it immediately at 6% per annum, compound interest payable half-yearly and thereby gains Rs. 45 at the end of the year. What was the sum borrowed?

  1. Rs. 50,000

  2. Rs. 40,500

  3. Rs. 55,000

  4. Rs. 60,000

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P be the sum. Simple interest at 6% is 0.06P. Compound interest half-yearly at 6% per annum (3% per half-year) for one year is P(1 + 0.03)^2 - P = P(1.0609) - P = 0.0609P. The gain is 0.0609P - 0.06P = 0.0009P. Setting 0.0009P = 45 gives P = 45 / 0.0009 = 50,000.

AI explanation

Let the sum be P. The man pays 6% of P in simple interest but earns P * (1 + 0.06/2)^2 - P in compound interest, gaining a difference of Rs. 45. The compound interest factor is 1.0609, so the gain is 0.0060P. Solving 0.0060P = 45 gives P = Rs. 50,000.

Keep practicing — related questions