Discussion

The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?

Answer: A

\[ \text{SI} = \frac{P \times R \times T}{100} \]

The time equals the rate, so write both as \( R \).

\[ \frac{4}{9}P = \frac{P \times R \times R}{100} \]

The \( P \) cancels:

\[ \frac{4}{9} = \frac{R^{2}}{100} \quad\Longrightarrow\quad R^{2} = \frac{400}{9} \]

\[ R = \frac{20}{3} = 6\tfrac{2}{3} \]

So the rate is \( 6\tfrac{2}{3}\% \) and the time \( 6\tfrac{2}{3} \) years.

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