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A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

Correct answer: A. 3.46%

  • A. 3.46%
  • B. 4.5%
  • C. 5%
  • D. 6%

Explanation

Let the original annual rate be r. The first Rs. 725 earns Rs. 725 x r for 1 year, while Rs. 362.50 lent for 4 months at twice the rate earns Rs. 362.50 x 2r x 4/12 = Rs. 241.67r. Thus Rs. 33.50 = Rs. 966.67r, giving r = 0.03465, or about 3.46% per annum. Option b, 4.5%, usually results from treating the second loan as earning interest for a full year.

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