Multiple choice

The compound interest and simple interest on a certain sum for 2 years, respectively, are Rs. 41 and Rs. 40. Find the sum and the rate.

  1. Rs.400, 5%

  2. Rs.450, 3%

  3. Rs. 500, 4%

  4. None of these
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A Correct answer
Explanation

Simple interest for 2 years is 40, so SI for 1 year is 20. Compound interest for 2 years is 41, so the extra 1 is the interest on the first year's interest (20). Rate = (1/20) * 100 = 5%. Since 20 is 5% of the sum, Sum = 20 / 0.05 = 400.

AI explanation

The difference between compound interest and simple interest for two years is calculated as Principal multiplied by Rate over 100 squared, which equals 41 minus 40 to give Re. 1. Substituting the rate as R, we have Principal multiplied by R squared equal to 10000. The simple interest for one year is Rs. 20, meaning Principal multiplied by R equals 2000, so dividing 10000 by 2000 gives a rate of 5% and substituting R back yields a principal of Rs. 400.

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