Multiple choice

The difference between SI and CI earned on a principal of Rs. 20,000 each in the first 2 years is Rs. 800. Find the rate of interest and total simple interest.

  1. 20% & Rs.4000

  2. 20% & Rs.8000

  3. 10% & Rs.8000

  4. 10% & Rs.4000
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B Correct answer
Explanation

Difference between CI and SI for 2 years is P * (r/100)^2. 800 = 20000 * (r/100)^2. 800/20000 = (r/100)^2. 0.04 = (r/100)^2. r/100 = 0.2, so r = 20%. Simple interest = P * r * t / 100 = 20000 * 0.2 * 2 = 8000.

AI explanation

Using the formula for the difference between compound and simple interest for 2 years, the difference equals (P times R squared) divided by 10000. Substituting the given values gives 20000 times R squared divided by 10000 equals 800, so R squared equals 400, meaning the rate is 20%. The total simple interest for 2 years is calculated as P times R times T divided by 100, which is 20000 times 20 times 2 divided by 100, equalling Rs. 8000.

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