Multiple choice

Simple interest on a certain sum is 9 over 25 of the sum. Find the rate per cent and time, if both are numerically equal.

  1. 6 %, 6 years

  2. 6 %, 8 years

  3. 8 %, 6 years

  4. 8 %, 8 years
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A Correct answer
Explanation

Simple Interest (SI) = (P * R * T) / 100. Given SI = (9/25)P and R = T. So, (9/25)P = (P * R * R) / 100. This simplifies to R^2 = (9 * 100) / 25 = 36. Thus, R = 6% and T = 6 years.

AI explanation

Using the simple interest formula, Simple Interest equals Principal times Rate times Time divided by 100. We are given that the interest is 9/25 of the principal, so (Principal x Rate x Rate) / 100 = 9/25 x Principal. Canceling the principal and multiplying both sides by 100 gives Rate squared = 900/25 = 36. Taking the square root provides a rate of 6 percent, and since the rate and time are numerically equal, the time is 6 years.

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