Reena took a loan of Rs. 1200 at simple interest for as many years as the numerical value of the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest per annum?

Introduction / Context:
This question is a classic simple interest problem where the time in years is numerically equal to the rate of interest in percent. You are given the principal and the total interest paid and asked to find the rate. Such problems rely on the simple interest formula and the relationship between time and rate, and they are very common in competitive exams testing basic financial arithmetic.

Given Data / Assumptions:

• Principal (P) = Rs. 1200.

• Simple interest (SI) paid = Rs. 432.

• Time (T) in years is equal to the rate of interest (R) in percent.

• Interest is calculated using simple interest, not compound interest.

Concept / Approach:
The simple interest formula is SI = (P * R * T) / 100. Here, we are told that T = R. This allows us to substitute T with R, leading to SI = (P * R^2) / 100. We already know SI and P, so we can solve this equation for R^2 and then for R. Since R represents a positive percentage rate, we choose the positive square root of R^2.

Step-by-Step Solution:
Step 1: Write the simple interest formula: SI = (P * R * T) / 100. Step 2: Given T = R, substitute T with R, so SI = (P * R * R) / 100 = (P * R^2) / 100. Step 3: Substitute the known values: SI = 432 and P = 1200. Step 4: 432 = (1200 * R^2) / 100. Step 5: Simplify the right side: (1200 / 100) = 12, so 432 = 12 * R^2. Step 6: Divide both sides by 12: R^2 = 432 / 12 = 36. Step 7: Therefore, R = square root of 36 = 6 (taking positive value, since rate cannot be negative in this context). Step 8: Hence, the rate of interest per annum is 6%.

Verification / Alternative check:
If R = 6%, then T = R = 6 years. Using the basic SI formula: SI = (P * R * T) / 100 = (1200 * 6 * 6) / 100. Compute: 6 * 6 = 36, so SI = (1200 * 36) / 100 = 43,200 / 100 = Rs. 432. This matches the given interest exactly, confirming that the rate is 6% per annum.

Why Other Options Are Wrong:
• 3.6%: If R = 3.6%, then T would also be 3.6 years, and the interest computed would not equal Rs. 432.
• 18%: If R = 18%, then T would be 18 years, giving a much larger interest than Rs. 432 for a principal of Rs. 1200.
• Cannot be determined: The information provided is sufficient to uniquely determine the rate, so this option is incorrect.

Common Pitfalls:
Some students misinterpret the phrase "for as many years as the rate of interest" and treat time and rate as independent values. Others may forget to square R when substituting T = R into the simple interest formula. Using the relation SI = (P * R^2) / 100 and solving carefully for R^2 ensures the correct answer. Always remember to interpret such wording as T = R in numerical value.

Final Answer:
The rate of interest per annum charged on Reena's loan was 6%.