Multiple choice

A sum of money was borrowed at $6\%$ per annum simple interest. At the end of first year Rs. $6800$ was paid of and the rate of interest on the balance was reduced to $5\%$ per annum. If the interest for the second year was $\displaystyle \frac{11}{20}$ of the interest for the first year what was the original sum borrowed?

  1. Rs. $10000$
  2. Rs. $12000$
  3. Rs. $17000$
  4. Rs. $15000$
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C Correct answer
AI explanation

Let the original sum borrowed be P, making the first year's simple interest at 6% equal to 0.06P. After paying off Rs. 6800, the outstanding balance for the second year is (P + 0.06P - 6800), and the interest on this balance at 5% is 0.05(1.06P - 6800). We are given that this second year's interest is 11/20 of the first year's interest, so 0.05(1.06P - 6800) = (11/20) * 0.06P. Expanding and simplifying this equation gives 0.053P - 340 = 0.033P, which leads to 0.02P = 340; solving this results in an original sum of Rs. 17000.

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