Multiple choice

Mr. Sherpal lends a sum of money to Mr. Kapoor at a certain rate of interest for two years. He is confused whether to lend at simple interest or compound interest. The total compound interest on the amount would be Rs. 1080, whereas the total simple interest would be Rs. 960. What will be the rate if the sum is lend in such a way that simple interest becomes Rs. 3000 and the total number of years is equal to the rate per annum?

  1. 10.5%

  2. 12.5%

  3. 25.0%

  4. 15.5%

  5. 8.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2 years, CI - SI = P(r/100)^2. 1080 - 960 = 120 = P(r/100)^2. Also SI = P*r*T/100 = 960 = P*r*2/100 => P*r = 48000. So P = 48000/r. 120 = (48000/r) * (r^2/10000) = 4.8r. r = 120/4.8 = 25. The second part of the question asks for rate if SI = 3000 and T = r. SI = P*r*r/100 = 3000. Using P = 48000/25 = 1920. 1920 * r^2 / 100 = 3000 => r^2 = 300000/1920 = 156.25. r = 12.5.

AI explanation

The difference between compound interest and simple interest for two years on the same principal and rate is given by the formula Difference = P(R/100)^2, so 1080 - 960 = P(R/100)^2 which simplifies to 120 = P(R/100)^2. The simple interest for two years is P times R times 2/100 = 960, giving P times R = 48000, and substituting this into the first equation yields R = 25%. The question asks for the rate if the simple interest is Rs. 3000 and the number of years equals the rate, so using the formula S.I. = (P times R times T)/100 with T equal to R and P = 48000/25 gives 3000 = (1920 times R^2)/100, which simplifies to 3000 = 19.2 times R^2, resulting in a rate of 12.5%.

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