Simple interest on a certain sum for 8 months at 6% per annum is Rs 340. What is the value of the principal sum, in rupees?

Introduction / Context:
This question requires working backwards from the simple interest earned to find the original principal. Such reverse calculations are common when a bank statement shows interest credited for a partial year and a customer wants to know what principal produced that interest at a known annual rate. It reinforces the idea that the simple interest formula can be algebraically rearranged to solve for any one of its variables.

Given Data / Assumptions:

Simple interest I = Rs 340
Annual simple interest rate R = 6 percent per annum
Time T = 8 months
Interest is calculated using simple interest
We need to find the principal P

Concept / Approach:
The simple interest formula is I = P * R * T, where R is in decimal form and T is in years. Since the time is given in months, convert 8 months into a fraction of a year. Then rearrange the formula to solve for P: P = I / (R * T). Substitute the known values and compute the principal. This demonstrates how time in months affects the total interest on a given sum.

Step-by-Step Solution:
Step 1: Convert the annual rate to decimal. R = 6 percent = 6 / 100 = 0.06. Step 2: Convert the time from months to years. T = 8 months = 8 / 12 years = 2 / 3 years. Step 3: Start from the simple interest formula I = P * R * T. 340 = P * 0.06 * (2 / 3). Step 4: Simplify the product of R and T. 0.06 * (2 / 3) = 0.06 * 0.6667 ≈ 0.04. More exactly, 6 / 100 * 2 / 3 = 12 / 300 = 4 / 100 = 0.04. Step 5: So the equation is 340 = P * 0.04. Step 6: Solve for P: P = 340 / 0.04. Step 7: P = 8,500 rupees.

Verification / Alternative check:
To check, compute the interest on 8,500 rupees at 6 percent per annum for 8 months. First, annual interest on 8,500 at 6 percent is 8,500 * 0.06 = 510 rupees. Since 8 months is 8 / 12 of a year, the interest is 510 * (8 / 12) = 510 * 2 / 3 = 340 rupees. This matches the given interest, confirming that the principal is correctly calculated as 8,500 rupees.

Why Other Options Are Wrong:
If the principal were Rs 9,500, simple interest for 8 months at 6 percent per annum would be greater than 340 rupees. A principal of Rs 8,000 would give annual interest of 480 rupees and 8 month interest of 320 rupees, which is too low. A principal of Rs 6,800 would produce even less interest. Only a principal of 8,500 rupees yields exactly 340 rupees of interest under the given rate and time.

Common Pitfalls:
Learners sometimes forget to convert months to years and instead treat T as 8, which inflates the principal estimate. Others may incorrectly approximate the fraction 8 / 12 or make arithmetic mistakes when dividing 340 by 0.04. Carefully converting the time unit and simplifying the fraction for the product R * T helps maintain accuracy in such reverse interest problems.

Final Answer:
The principal sum invested or borrowed is Rs 8,500.