A person invests a certain sum of money for two years at an annual rate of 8% and finds that the amount received under compound interest is Rs 48 more than the amount that would have been received under simple interest. What is the original principal sum invested?

Introduction / Context:
This problem compares compound interest and simple interest on the same principal, rate, and time. The extra amount earned under compound interest, compared to simple interest, helps us back calculate the original principal. Such questions are common in aptitude exams to test understanding of how compound interest grows faster than simple interest over multiple years.

Given Data / Assumptions:

• The principal sum is P (unknown).
• Rate of interest, R = 8% per annum.
• Time period, T = 2 years.
• Difference between compound interest and simple interest over 2 years is Rs 48.
• Interest is compounded annually for the compound interest calculation.

Concept / Approach:
Simple interest for T years is:
SI = (P * R * T) / 100Compound interest for 2 years at rate R% per annum (compounded annually) can be written using the amount formula A = P * (1 + R/100)^2, and CI = A - P. For 2 years, there is a helpful shortcut for the difference between CI and SI:
Difference (CI - SI) for 2 years = P * (R^2) / (100^2)Using this relationship makes the calculation straightforward.

Step-by-Step Solution:
Step 1: Use the known relation for the difference.CI - SI = P * (R^2) / (100^2)Step 2: Substitute R = 8%.CI - SI = P * (8^2) / (100^2) = P * 64 / 10,000Step 3: Simplify the fraction.64 / 10,000 = 0.0064So, CI - SI = 0.0064 * PStep 4: Equate this to the given difference.0.0064 * P = 48Step 5: Solve for P.P = 48 / 0.0064 = 7,500Thus, the original principal is Rs 7,500.

Verification / Alternative check:
We can verify by computing both SI and CI explicitly. Simple interest for 2 years: SI = (7500 * 8 * 2) / 100 = (7500 * 16) / 100 = Rs 1,200. Amount by SI = 7500 + 1200 = Rs 8,700. Compound amount for 2 years: A = 7500 * (1 + 8/100)^2 = 7500 * 1.08^2 = 7500 * 1.1664 = Rs 8,748. CI = 8,748 - 7,500 = Rs 1,248. The difference CI - SI = 1,248 - 1,200 = Rs 48, exactly as given, so the principal is correct.

Why Other Options Are Wrong:

• Rs 8,000 would give a larger difference than Rs 48 because the extra compound interest scales with principal.
• Rs 6,500 and Rs 5,000 would produce smaller differences between CI and SI, not matching the given Rs 48.

Common Pitfalls:
Many learners try to compute full CI and SI without using the shortcut formula for the difference, which can lead to arithmetic mistakes. Another common error is to confuse the formula for CI - SI over 2 years with that over 3 years, where an additional term appears. Remember that for exactly 2 years, the difference is P * R^2 / 100^2, which is quick and reliable for exam conditions.

Final Answer:
The original principal sum of money invested by the person is Rs 7,500.