In a simple interest calculation in quantitative aptitude, 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 simple interest received is greater by Rs. 840. What is the value of the original principal sum that was invested?

Introduction / Context:
This aptitude question tests the basic relationship between principal, rate, time, and simple interest, and how a change in rate of interest affects the total interest earned. By comparing the interest at two different rates for the same principal and time period, we can back-calculate the value of the original principal sum from the given difference in interest, here Rs. 840.

Given Data / Assumptions:

• The same principal sum P is invested for 2 years.
• First case: rate of simple interest R1 = 18% per annum.
• Second case: rate of simple interest R2 = 12% per annum.
• Time T is the same in both cases and equals 2 years.
• Extra interest earned at the higher rate is Rs. 840.
• We assume ordinary simple interest: SI = (P * R * T) / 100.

Concept / Approach:
The key idea is that the extra interest arises only from the difference in rates, since principal and time remain the same. Therefore, we can write the difference of interests directly in terms of the difference in rates and equate it to Rs. 840 in order to find the principal P.

Step-by-Step Solution:
Simple interest formula: SI = (P * R * T) / 100. Interest at 18%: SI1 = (P * 18 * 2) / 100. Interest at 12%: SI2 = (P * 12 * 2) / 100. Difference in interest: SI1 - SI2 = Rs. 840. Compute SI1 - SI2 using rates: SI1 - SI2 = P * (18 - 12) * 2 / 100 = P * 6 * 2 / 100. So, P * 12 / 100 = 840. Therefore, P = 840 * 100 / 12. P = 840 * (100 / 12) = 840 * (25 / 3) = 7000. Hence, the original principal sum is Rs. 7000.
Verification / Alternative check:
We can quickly verify: At 12% for 2 years, interest = 7000 * 12 * 2 / 100 = 1680. At 18% for 2 years, interest = 7000 * 18 * 2 / 100 = 2520. Difference = 2520 - 1680 = 840, which matches the given excess interest. Therefore, Rs. 7000 is correct.

Why Other Options Are Wrong:
Rs. 5600, Rs. 6300, Rs. 8400, and Rs. 9000 all produce a difference of interest at 18% and 12% over 2 years that is not exactly Rs. 840. Each of these values either gives a smaller or larger difference than 840, so they cannot satisfy the equation based on the simple interest formula.

Common Pitfalls:
A common mistake is to compute each full interest amount separately without focusing on the difference in rates, which leads to unnecessary calculations. Another error is to forget the factor of time T = 2 years when forming the difference. Some students also divide by the wrong percentage or misplace decimal points when working with percentages, which changes the final value of P.

Final Answer:
The original principal sum invested is Rs. 7000.