What principal amount will yield simple interest of Rs 120 at a rate of 6% per annum over a period of 10 years, assuming that interest is calculated using the standard simple interest formula for the entire duration?

Introduction / Context:
This is a simple reverse calculation question on simple interest. The simple interest earned, the rate of interest, and the time period are given. The task is to find the principal that would generate this interest. Such problems are very common in the early stages of quantitative aptitude practice and build familiarity with rearranging the simple interest formula to make the principal the subject of the formula.

Given Data / Assumptions:

• Simple interest SI = Rs 120.
• Rate of interest R = 6% per annum.
• Time period T = 10 years.
• Principal P is unknown.
• Interest is calculated using simple interest for the full duration.

Concept / Approach:
The simple interest formula is:
SI = (P * R * T) / 100 To find the principal P, we rearrange the formula as:
P = (SI * 100) / (R * T) By substituting SI = 120, R = 6, and T = 10, we can compute the value of P directly through straightforward arithmetic. It is useful to simplify R * T first, then divide SI * 100 by this product.

Step-by-Step Solution:
Given SI = Rs 120, R = 6% per annum, T = 10 years. Use the rearranged formula: P = (SI * 100) / (R * T). Compute R * T = 6 * 10 = 60. Compute SI * 100 = 120 * 100 = 12000. Now divide: P = 12000 / 60. P = 200. Therefore, the required principal amount is Rs 200.

Verification / Alternative check:
We can verify by calculating the simple interest on Rs 200 at 6% per annum for 10 years. SI = (200 * 6 * 10) / 100. Compute 6 * 10 = 60, so SI = (200 * 60) / 100 = 12000 / 100 = 120. This matches the given interest, confirming that Rs 200 is the correct principal.

Why Other Options Are Wrong:
If P were Rs 120, simple interest would be (120 * 6 * 10) / 100 = 72, which is less than 120.
If P were Rs 180, SI would be 108, still not 120.
If P were Rs 210, SI would be 126, which is more than 120.
If P were Rs 240, SI would be 144. Therefore these options do not match the given interest at the specified rate and time.

Common Pitfalls:
A common error is to forget to divide by 100 in the simple interest formula or to miscompute R * T. Some students invert the formula incorrectly and multiply by R * T instead of dividing by it. Others may confuse amount and interest, treating Rs 120 as the final amount instead of the interest. Writing out the formula clearly and substituting carefully helps to avoid these mistakes.

Final Answer:
The principal amount that will yield simple interest of Rs 120 at 6% per annum for 10 years is Rs 200.