At what rate of simple interest per annum can an amount of ₹ 1553.40 be obtained on the principal amount of ₹ 8630 after 3 years?

### Concept & Simple Interest Rate The problem asks for the rate of interest that yields an interest amount of ₹ $1553.40$. We use the standard rate formula: $$R = \frac{SI \times 100}{P \times T}$$ ### Step-by-Step Solution * Given Principal, $P = \text{₹ } 8630$ * Given Simple Interest, $SI = \text{₹ } 1553.40$ (Note: "amount of ₹ 1553.40 be obtained on the principal" implies this is the interest earned) * Given Time, $T = 3 \text{ years}$ * Substitute the values into the formula: $R = \frac{1553.40 \times 100}{8630 \times 3}$ $R = \frac{155340}{25890}$ $R = 6\%$ p.a. ### Exam Strategy & Shortcut Use unit digits for quick division: $2589 \times 6$: $9 \times 6 = 54$, which ends in 4, perfectly matching $15534$. This confirms $6\%$ without doing long division. Since $6\%$ is not an option, the answer is "None of these". ### Common Pitfall A student might misinterpret "an amount of ₹ 1553.40" as the final amount $A$ instead of the interest. However, since $1553.40$ is significantly less than the principal $8630$, logic dictates it must be the interest. ### Final Answer Therefore, the correct answer is **None of these**.