Multiple choice

The simple interest on a sum of money is $\dfrac49$of the principal and the number of years is equal to the rate of interest. The rate percent is-

  1. $3 \dfrac{1}{4}$
  2. $6 \dfrac{2}{3}$
  3. $6$
  4. $5$
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B Correct answer
Explanation

Simple interest is given by (P * R * T) / 100. We are told SI = (4/9)P and R = T. Substituting these gives (4/9)P = (P * R * R) / 100, which simplifies to R^2 = 400/9. Taking the square root, R = 20/3, which is 6 2/3 percent.

AI explanation

Using the simple interest formula Simple Interest = (Principal x Rate x Time) / 100, the interest is 4/9 of the principal, meaning (4/9) x Principal = (Principal x Rate x Rate) / 100. Canceling the principal from both sides gives Rate squared = 400/9. Taking the square root provides the rate of 6 2/3 percent.

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