Finding Simple Interest for a Fractional Rate and Time: What is the simple interest (SI) on ₹68,000 at 16 2/3% per annum for 9 months, assuming simple interest and that 16 2/3% is first converted into a usable fraction or decimal?

Introduction / Context:
This question involves a fractional rate of interest (16 2/3%) and a time period of less than one year (9 months). You must correctly convert both the mixed number percentage and the months into suitable forms and then apply the simple interest formula. This tests attention to detail in handling fractions and time conversions.

Given Data / Assumptions:

• Principal P = ₹68,000.
• Rate r = 16 2/3% per annum.
• Time t = 9 months.
• Simple interest is used.

Concept / Approach:
First, convert the mixed percentage 16 2/3% into an improper fraction or decimal. Then convert 9 months into years because the simple interest formula uses years. Finally, apply SI = (P * r * t) / 100. Working carefully with fractions helps avoid calculator mistakes and improves understanding of proportional reasoning in interest calculations.

Step-by-Step Solution:
Step 1: Convert 16 2/3% to an improper fraction. 16 2/3 = (50 / 3)%. Step 2: In decimal form, (50 / 3)% ≈ 16.6667%, but we will keep it as 50 / 3 for cleaner algebra. Step 3: Convert 9 months to years: t = 9 / 12 = 3 / 4 years. Step 4: Use the SI formula: SI = (P * r * t) / 100. Step 5: Substitute values: SI = (68,000 * (50 / 3) * (3 / 4)) / 100. Step 6: Simplify: (50 / 3) * (3 / 4) = 50 / 4 = 12.5. Step 7: So SI = (68,000 * 12.5) / 100 = 68,000 * 0.125 = ₹8,500. Step 8: Therefore, the simple interest is ₹8,500.

Verification / Alternative check:
Note that 16 2/3% per year is 1 / 6 of the principal per year, since (16 2/3) / 100 = 1 / 6. For 9 months, which is 3 / 4 of a year, the interest is P * (1 / 6) * (3 / 4) = P / 8. Here, P / 8 = 68,000 / 8 = ₹8,500, confirming the previous calculation.

Why Other Options Are Wrong:

• ₹7,500 and ₹8,000: Both are less than P / 8 and correspond to using incorrect fractions or time conversions.
• ₹9,500: Larger than P / 8, indicating an overestimation of either the rate or time.
• ₹6,500: Far too low and not equal to P / 8.

Common Pitfalls:
Many candidates misconvert 16 2/3% as 16.23% or 16.33% instead of 16.6667%. Others forget to convert 9 months to years and use t = 9, which greatly inflates the interest. Always express mixed fractions correctly and convert months into years when using standard interest formulas.

Final Answer:
The simple interest on ₹68,000 is ₹8,500.