In a simple interest calculation, a certain principal sum is invested at 18% per annum for 2 years instead of at 12% per annum for the same time period, and therefore the interest received is greater by Rs. 840. What is the value of the original principal sum?

Introduction / Context:
This aptitude question tests the concept of simple interest when the same principal is invested at two different rates of interest for the same time period. Instead of directly giving the principal amount, the question tells us how much extra interest is obtained when the higher rate is used. Our task is to use the relationship between rate, time, and interest to calculate the original sum invested. Such questions are common in banking and competitive exams and help students understand how changes in rate affect interest earned.

Given Data / Assumptions:
- Let the principal sum be P rupees.
- Time period in both cases = 2 years.
- First rate of simple interest = 18 percent per annum.
- Second rate of simple interest = 12 percent per annum.
- Extra interest received due to using 18 percent instead of 12 percent for 2 years = Rs. 840.
- Interest is calculated using the simple interest formula only, with no compounding.

Concept / Approach:
Under simple interest, interest is directly proportional to principal, rate, and time. The basic formula is:
Simple interest SI = (P * R * T) / 100, where P is principal, R is rate in percent per annum, and T is time in years. When the same principal and time are used but at different rates, the difference in simple interest is due only to the difference in rates. Therefore, we can write an equation using the difference in rates multiplied by principal and time to match the given extra interest of Rs. 840.

Step-by-Step Solution:
Step 1: Write the expression for simple interest at 18 percent per annum for 2 years: SI1 = (P * 18 * 2) / 100. Step 2: Write the expression for simple interest at 12 percent per annum for 2 years: SI2 = (P * 12 * 2) / 100. Step 3: The extra interest earned by using 18 percent instead of 12 percent is SI1 - SI2. This is equal to Rs. 840. Step 4: Compute the difference: SI1 - SI2 = P * (18 - 12) * 2 / 100 = P * 6 * 2 / 100 = P * 12 / 100. Step 5: Set up the equation: (12 * P) / 100 = 840. So P = 840 * 100 / 12. Step 6: Simplify: 840 * 100 = 84000 and 84000 / 12 = 7000. Therefore, P = Rs. 7000.

Verification / Alternative check:
If the principal is Rs. 7000, interest at 18 percent for 2 years is SI1 = 7000 * 18 * 2 / 100 = 7000 * 36 / 100 = Rs. 2520. Interest at 12 percent for 2 years is SI2 = 7000 * 12 * 2 / 100 = 7000 * 24 / 100 = Rs. 1680. The difference is 2520 - 1680 = Rs. 840, which matches the given extra interest. This confirms that the principal amount of Rs. 7000 is correct.

Why Other Options Are Wrong:
Rs. 5600 gives a smaller difference in interest that is less than Rs. 840. Rs. 6300 produces a difference that is close but not exactly Rs. 840. Rs. 8400 and Rs. 9000 produce interest differences larger than Rs. 840. Only Rs. 7000 satisfies the exact condition given in the problem statement.

Common Pitfalls:
A common mistake is to compute the interest for each rate separately without using the difference in rates formula, which leads to longer calculations. Another frequent error is using 6 percent only once instead of multiplying by 2 years, or forgetting to divide by 100 when using the percentage formula. Some learners also confuse simple interest with compound interest, but here the interest is clearly simple interest only.

Final Answer:
The required principal sum is Rs. 7000.