In aptitude (Simple Interest), a sum earns a total simple interest of ₹9,648 at the rate of 12% per annum in 6 years. What is the principal sum (in ₹) on which this interest is earned?

Introduction / Context:
This is a direct application of the simple interest formula where total interest, rate, and time are given and you must find the original principal. Such problems are very common in quantitative aptitude exams and are designed to test your speed and accuracy with percentage calculations and algebraic rearrangement.

Given Data / Assumptions:

• Total simple interest SI = ₹9,648.
• Annual interest rate r = 12% per annum.
• Time period t = 6 years.
• We need to determine the principal P in rupees.
• Interest is calculated under simple interest, not compound interest.

Concept / Approach:
The basic simple interest formula is: SI = (P * r * t) / 100. Here SI is the interest amount, P is the principal, r is the rate in percent, and t is time in years. When SI, r, and t are known, we rearrange the formula to find P: P = (SI * 100) / (r * t). The key is to substitute correctly and simplify step by step.

Step-by-Step Solution:
Step 1: Start with SI = (P * r * t) / 100. Step 2: Substitute SI = 9,648, r = 12, and t = 6. Step 3: 9,648 = (P * 12 * 6) / 100. Step 4: Multiply rate and time: 12 * 6 = 72. Step 5: So 9,648 = (P * 72) / 100. Step 6: Rearrange for P: P = 9,648 * 100 / 72. Step 7: Compute 9,648 * 100 = 964,800. Step 8: Divide 964,800 by 72 to get P = 13,400. Step 9: Therefore, the principal sum is ₹13,400.

Verification / Alternative check:
Verify by recomputing SI using P = ₹13,400, r = 12%, t = 6 years: SI = (13,400 * 12 * 6) / 100. Compute 13,400 * 12 = 160,800. Then 160,800 * 6 = 964,800. Finally, divide by 100: 964,800 / 100 = 9,648. The simple interest matches the given value, confirming the principal is correct.

Why Other Options Are Wrong:
₹16,080, ₹10,720, ₹8,040, and ₹12,000 all produce simple interest amounts that differ from ₹9,648 when plugged into the formula with r = 12% and t = 6 years. Only the principal of ₹13,400 yields exactly the specified interest.

Common Pitfalls:
Some students mistakenly divide by r or t alone instead of the product r * t, or forget to multiply by 100. Another error is miscalculating the product 12 * 6 or the division step at the end. Writing each arithmetic step clearly reduces the risk of such mistakes during time pressured exams.

Final Answer:
The sum on which a simple interest of ₹9,648 is earned at 12% per annum for 6 years is ₹13,400.