Explanation:

- To solve this, let's represent the rate per cent as "R" and the time as "T".

- The problem states that the simple interest (SI) is 27% of the principal (P), so \(SI = \frac{27}{100} \times P\).

- Using the simple interest formula \(SI = \frac{P \times R \times T}{100}\), we can compare both expressions for SI.

- This gives us \(\frac{27}{100}P = \frac{P \times R \times T}{100}\), which simplifies to \(27 = R \times T\).

- It's also given that \(T = \frac{R}{3}\). Substitute this into the equation: \(27 = R \times \frac{R}{3}\).

- Solving \(27 = \frac{R^2}{3}\) results in \(R^2 = 81\), giving \(R = 9\).

- Therefore, the rate per cent is 9%.

Correct Answer: Option 3 - 9%