Multiple choice

Mahesh borrowed a certain sum for two years at simple interest from Bhim. Mahesh lent this sum to Vishnu at the same rate for two years compound interest. At the end of two years, Mahesh received Rs. $410$ as compound interest but paid Rs. $400$ as simple interest. Find the sum and rate of interest.

  1. $400,15\%$
  2. $5000,10\%$
  3. $4000,5\%$
  4. $7000,15\%$
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C Correct answer
Explanation

Simple interest for 2 years = 400, so SI for 1 year = 200. Compound interest for 2 years = 410. The difference is the interest on the first year's interest: 410 - 400 = 10. Rate = (10 / 200) * 100 = 5%. Principal = 200 / 0.05 = 4000.

AI explanation

Using the Simple Interest formula, 400 = (Principal x Rate x 2) / 100, which simplifies to Principal x Rate = 20000. The difference between the compound interest and the simple interest for 2 years is calculated as Principal x Rate squared, divided by 10000, so 410 - 400 equals 10. This means Principal x Rate squared equals 100000, and dividing this by the first equation gives a rate of 5%. Substituting the rate back into the first equation yields a principal of Rs. 4000.

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