In aptitude (Simple Interest), a certain sum amounts to ₹5,182 in 2 years and to ₹5,832 in 3 years at the same simple interest rate. What is the original principal amount (in ₹) invested at simple interest?

Introduction / Context:
This question uses two different future amounts at the same simple interest rate to help you work backwards and find the original principal. It highlights an important simple interest idea: the interest added each year is constant, so the difference between successive years amounts is equal to the interest for one year. Recognizing this shortcut can help you solve many banking and aptitude questions quickly.

Given Data / Assumptions:

• Amount after 2 years, A2 = ₹5,182.
• Amount after 3 years, A3 = ₹5,832.
• The interest rate is simple and unchanged throughout.
• Let the principal be P and the annual simple interest be I per year.
• We must find the principal P in rupees.

Concept / Approach:
Under simple interest, interest added every year is a fixed amount I. Thus: A2 = P + 2I A3 = P + 3I The difference between the amounts in consecutive years is: A3 - A2 = (P + 3I) - (P + 2I) = I So the increase from year 2 to year 3 directly gives the yearly interest I. Once I is known, we can use A2 = P + 2I to solve for the principal P without needing the rate explicitly.

Step-by-Step Solution:
Step 1: Compute the difference between the amounts for year 3 and year 2. Step 2: A3 - A2 = 5,832 - 5,182 = 650. Step 3: This difference equals the annual simple interest I, so I = ₹650 per year. Step 4: Use the 2 year amount expression A2 = P + 2I. Step 5: Substitute A2 = 5,182 and I = 650 into the equation: 5,182 = P + 2 * 650. Step 6: Compute 2 * 650 = 1,300. Step 7: Rearrange for P: P = 5,182 - 1,300 = 3,882. Step 8: Therefore the original principal is ₹3,882.

Verification / Alternative check:
We can verify by checking both years. From P = 3,882, year 1 interest is I = 650. Amount after 2 years: A2 = 3,882 + 2 * 650 = 3,882 + 1,300 = 5,182 Amount after 3 years: A3 = 3,882 + 3 * 650 = 3,882 + 1,950 = 5,832 Both match the given amounts exactly, confirming that ₹3,882 is correct.

Why Other Options Are Wrong:
₹4,000: This would give A2 = 4,000 plus 2 years of interest, which cannot equal 5,182 while keeping the same difference to reach 5,832.
₹2,882: This principal is too small and would require a much larger yearly interest than the 650 implied by the difference of 650 between A2 and A3.
₹5,000 and ₹3,500: Both fail to produce the correct pair of amounts 5,182 and 5,832 when combined with a constant annual interest value.

Common Pitfalls:
Learners sometimes try to find the interest rate first using complicated algebra instead of noticing that the difference between consecutive yearly amounts is simply the annual interest. Another common mistake is subtracting in the wrong order, leading to a negative interest, or using the 3 year amount expression incorrectly. Always remember that under simple interest, the difference between amounts in successive years is constant and equal to the yearly interest. Use that fact to simplify problems like this.

Final Answer:
The principal amount invested at simple interest is ₹3,882.