Multiple choice

Simple interest on a certain sum at a certain annual rate of interest is $\dfrac{1}{9}$. If the numbers representing rate percent and time in years be equal, then rate of interest is :

  1. $3\dfrac{1}{3}\%$
  2. $5\%$
  3. $6\dfrac{2}{3}\%$
  4. $10\%$
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A Correct answer
Explanation

SI = P*R*T/100. SI = P/9. So P/9 = P*R*T/100. 1/9 = R*T/100. Given R=T, 1/9 = R^2/100. R^2 = 100/9. R = 10/3 = 3 1/3%.

AI explanation

Let the sum be P, and let the rate percent and time in years be x. The simple interest formula is SI = (P * R * T) / 100, so P/9 = (P * x * x) / 100. This simplifies to x^2 = 100/9, which gives x = 10/3. The rate of interest is 10/3 percent, or 3 1/3 percent.

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