Multiple choice

The simple interest on a sum of money is $\dfrac {1}{9}$ of the principal, and the number of years is equal to the rate per cent per annum. Find the rate per cent

  1. $3$%
  2. $3\dfrac {1}{3}$%
  3. $10$%
  4. $\dfrac {1}{3}$%
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B Correct answer
Explanation

Simple interest SI = (P * R * T) / 100. Given SI = P/9 and R = T. So, P/9 = (P * R * R) / 100. This simplifies to R^2 = 100/9, so R = 10/3 = 3.33%.

AI explanation

Using the simple interest formula, Simple Interest = (Principal * Rate * Time) / 100, let the principal be P and the rate be R. Since the number of years equals the rate, we have (P/9) = (P * R * R) / 100. Canceling P from both sides gives R^2 = 100/9, so R = 10/3. The result is 3 1/3%.

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