A certain sum amounts to Rs 7350 in 2 years and to Rs 8575 in 3 years at the same compound interest rate. Find the original sum of money (principal) and hence determine the principal from the given options.

Introduction:
This compound interest question gives you two future amounts of the same principal at the same interest rate but for different times. Using these, you can first deduce the annual growth factor and then work backwards to find the original principal. It trains you to use ratios instead of directly solving for the rate first.

Given Data / Assumptions:

• Amount after 2 years (A2) = Rs 7350.
• Amount after 3 years (A3) = Rs 8575.
• Same compound interest rate for all years.
• Interest is compounded annually.
• We must find the principal P.

Concept / Approach:
Under compound interest, amounts after 2 and 3 years are A2 = P * (1 + r)^2 and A3 = P * (1 + r)^3, where r is the annual rate in decimal form. Dividing A3 by A2 cancels P, leaving (1 + r). Then you can substitute back into A2 or A3 to solve for P directly.

Step-by-Step Solution:
A2 = P * (1 + r)^2 = 7350A3 = P * (1 + r)^3 = 8575Divide A3 by A2:A3 / A2 = (1 + r)^3 / (1 + r)^2 = 1 + rSo 1 + r = 8575 / 7350Simplify 8575 / 7350 = 1.166666..., which is 7/6Hence 1 + r = 7/6, so r = 1/6 = 16 2/3% per annumNow find P using A2: 7350 = P * (7/6)^2 = P * 49/36Therefore P = 7350 * 36 / 49P = 7350 * (36/49) = Rs 5400

Verification / Alternative Check:
Using P = 5400 and r = 16 2/3%, we can check the amounts. After 2 years: P * (7/6)^2 = 5400 * 49/36 = 7350. After 3 years: P * (7/6)^3 = 5400 * 343/216 = 8575. Both values match the given amounts, confirming that P is correct.

Why Other Options Are Wrong:
Rs 3400, Rs 4400, Rs 6400 and Rs 4200: None of these values, when combined with a single consistent interest rate, give both 7350 after 2 years and 8575 after 3 years. Each fails at least one of the two conditions.

Common Pitfalls:
A common mistake is to attempt to calculate the rate directly without using the ratio method, which can lead to messy equations. Another is to misinterpret the amounts as including additional deposits or withdrawals, which is not stated in the question. Remember that under pure compound interest, the ratio of amounts at times differing by 1 year directly gives the growth factor 1 + r.

Final Answer:
The original principal that grows to Rs 7350 in 2 years and Rs 8575 in 3 years is Rs 5400.