Raghu invests Rs 1000 at a simple interest rate of 6% per annum and receives a total amount of Rs 1300 after X years. Using the standard simple interest formula, determine the value of X, that is, the number of years for which the money was invested until the amount became Rs 1300.

Introduction / Context:
This problem checks basic understanding of simple interest and how to work backward from the final amount to find the time period. Instead of asking for interest directly, the question gives the principal, rate, and final amount and asks for the duration of the investment. Such questions appear frequently in bank exams, SSC exams, and other aptitude tests where candidates must be very comfortable with the simple interest formula and rearranging it to isolate any required variable.

Given Data / Assumptions:

• Principal invested by Raghu, P = Rs 1000.
• Rate of simple interest, R = 6% per annum.
• Number of years of investment, T = X years (unknown).
• Total amount received after X years, A = Rs 1300.
• Interest is calculated using simple interest for the entire period.

Concept / Approach:
The simple interest formula is:
Simple interest (SI) = (P * R * T) / 100 The final amount with simple interest is:
Amount A = P + SI In this problem, A and P are known, so SI can first be found as A − P. Once SI is known, we can substitute SI, P, and R into the simple interest formula and solve for T. This involves only basic algebra, rearranging a linear equation in one variable.

Step-by-Step Solution:
Given principal P = Rs 1000. Given rate R = 6% per annum. Amount after X years A = Rs 1300. First, find the simple interest earned: SI = A − P = 1300 − 1000 = Rs 300. Use the simple interest formula: SI = (P * R * T) / 100. So, 300 = (1000 * 6 * T) / 100. Simplify the right side: (1000 * 6) / 100 = 60, so 300 = 60T. Therefore, T = 300 / 60 = 5 years. Hence, Raghu invested the money for 5 years.

Verification / Alternative check:
We can verify the result by computing the amount for 5 years directly. Simple interest for 5 years at 6% per annum on Rs 1000 is SI = (1000 * 6 * 5) / 100 = 300. The final amount after 5 years is P + SI = 1000 + 300 = Rs 1300, which matches the given amount. Therefore, the solution is verified as correct.

Why Other Options Are Wrong:
If X were 4 years, interest would be (1000 * 6 * 4) / 100 = Rs 240, giving an amount of only Rs 1240.
If X were 3 years, interest would be Rs 180, so the amount would be Rs 1180, which is too small.
If X were 2 years, interest would be Rs 120, so the amount would be Rs 1120.
If X were 6 years, interest would be Rs 360, leading to an amount of Rs 1360, which is larger than Rs 1300. Hence those options do not match the problem data.

Common Pitfalls:
A common mistake is to misread the given amount as interest rather than the total amount, which leads to an incorrect equation. Another error is to forget to subtract principal from amount to obtain the interest. Some students also mishandle the division when solving for T, especially when simplifying (P * R) / 100. Writing each step clearly prevents calculation errors and builds accuracy.

Final Answer:
Therefore, the money was invested for 5 years in order to grow from Rs 1000 to Rs 1300 at 6% simple interest per annum.