1. **State the problem:** Find the rate of interest per annum when the simple interest (SI) on 800 for 3 years is 54. 2. **Formula for simple interest rate:** $$ R = \frac{SI \times 100}{P \times T} $$ where $R$ is the rate of interest per annum, $SI$ is the simple interest, $P$ is the principal amount, and $T$ is the time in years. 3. **Substitute the given values:** $$ R = \frac{54 \times 100}{800 \times 3} $$ 4. **Calculate the denominator:** $$ 800 \times 3 = 2400 $$ 5. **Simplify the fraction:** $$ R = \frac{54 \times 100}{2400} = \frac{5400}{2400} $$ 6. **Cancel common factors:** $$ R = \frac{\cancel{5400}^{\div 300}}{\cancel{2400}^{\div 300}} = \frac{18}{8} $$ 7. **Simplify the fraction further:** $$ R = \frac{18}{8} = \frac{9}{4} = 2.25 $$ 8. **Interpret the result:** The rate of interest per annum is $2.25\%$, which matches option (B) $2 \frac{1}{4}\%$. **Final answer:** $2 \frac{1}{4}\%$ (Option B)