Multiple choice

Pratap borrowed a sum of money from Arun at simple interest, at the rate of $12\%\,p.a.$ for the first three years, $16\%\,p.a.$ for the next five years and $20\%\,p.a.$ for a period beyond eight years. If at the end of $11$ years, the total interest is $Rs.\,6080$ more than the sum, what was the sum borrowed?

  1. $\;Rs.\,3000$.
  2. $\;Rs.\,8000$.
  3. $\;Rs.\,7000$.
  4. $\;Rs.\,4000$.
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B Correct answer
Explanation

Let the sum be P. Interest = (P * 0.12 * 3) + (P * 0.16 * 5) + (P * 0.20 * 3) = 0.36P + 0.80P + 0.60P = 1.76P. We are given 1.76P = P + 6080, so 0.76P = 6080. P = 6080 / 0.76 = 8000.

AI explanation

Let the sum be P. The total interest for 11 years consists of 3 years at 12%, 5 years at 16%, and the remaining 3 years at 20%. The overall interest percentage is (3 x 12) + (5 x 16) + (3 x 20) = 36 + 80 + 60 = 176%. Since this interest is Rs. 6080 more than the sum, the excess interest percentage over the principal is 176% minus 100% = 76%. Solving 76% of P = 6080 yields P = Rs. 8000.

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