Praveena takes a loan of Rs 1,200 at simple interest for as many years as the numerical value of the rate of interest; if she pays a total of Rs 432 as interest at the end of the loan period, what is the annual simple interest rate in percent per annum?

Introduction / Context:
This simple interest question links the time of a loan and the rate of interest by saying that the number of years is equal to the numerical value of the rate. Such questions test a candidate's ability to form an equation from the symbolic statement and then solve for the rate using the simple interest formula. The situation is realistic for bank loans and small personal borrowings in aptitude exams.

Given Data / Assumptions:
- Principal borrowed P = Rs 1,200. - Total simple interest paid SI = Rs 432. - Let the annual simple interest rate be R percent. - Time period T in years is equal to the numerical value of R, so T = R years. - Interest is calculated using the simple interest formula only.

Concept / Approach:
The standard simple interest formula is SI = (P * R * T) / 100. Here, the key relationship is T = R. Substituting T with R in the formula gives SI = (P * R * R) / 100, which is SI = (P * R^2) / 100. Using the known values of SI and P, we can solve for R^2 and then take the positive square root to get the annual simple interest rate in percent.

Step-by-Step Solution:
Step 1: Write the simple interest formula: SI = (P * R * T) / 100. Step 2: Use the condition T = R, so SI = (P * R^2) / 100. Step 3: Substitute known values: 432 = (1,200 * R^2) / 100. Step 4: Multiply both sides by 100 to clear the denominator: 432 * 100 = 1,200 * R^2. Step 5: Compute the left side: 432 * 100 = 43,200. Step 6: Divide both sides by 1,200: R^2 = 43,200 / 1,200 = 36. Step 7: Take the positive square root (rate cannot be negative): R = square root of 36 = 6. Step 8: Therefore, the annual simple interest rate is 6 percent per annum.

Verification / Alternative check:
To verify, use R = 6 percent and T = 6 years in the simple interest formula. Compute SI = (1,200 * 6 * 6) / 100. First 1,200 * 6 = 7,200, then 7,200 * 6 = 43,200. Dividing by 100 gives SI = Rs 432. This matches the given interest, so the calculated rate of 6 percent per annum is correct.

Why Other Options Are Wrong:
A rate of 7 percent would give SI = (1,200 * 7 * 7) / 100 = 588, which is larger than Rs 432. A rate of 9 percent gives SI = (1,200 * 9 * 9) / 100 = 972, which is also incorrect. A rate of 11 percent produces even higher interest, far from the given Rs 432. Only 6 percent leads to exactly the required interest amount.

Common Pitfalls:
Learners sometimes treat T as 1 year or misread the statement and take T equal to interest instead of the numerical value of the rate. Another frequent error is to forget that R is in percent, which leads to missing the division by 100 in the formula. Ensuring that the relationship T = R is used correctly and carefully handling the equation avoids these mistakes.

Final Answer:
The annual simple interest rate on Praveena's loan is 6% per annum.