A certain sum amounts to Rs. 7350 in 2 years and to Rs. 8575 in 3 years at compound interest. Find the original sum invested.

Introduction / Context:
This question uses the fact that under compound interest, the amount after each equal time interval is multiplied by the same growth factor. We are given successive amounts at the end of 2 and 3 years and must work backwards to find the initial principal using the ratio of these two amounts.

Given Data / Assumptions:

• Amount after 2 years, A2 = Rs. 7350.
• Amount after 3 years, A3 = Rs. 8575.
• Interest is compounded annually at a constant rate.
• We must find the original principal P.

Concept / Approach:

In compound interest, A = P * (1 + r / 100)^n. Therefore A3 / A2 = (1 + r / 100)^(3) / (1 + r / 100)^(2) = 1 + r / 100. This ratio lets us find the yearly growth factor. Once we know 1 + r / 100, we can express A2 in terms of P and solve for the principal.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Rs. 3400, Rs. 4400, and Rs. 6400 do not produce the given pair of amounts when grown at a single constant compound interest rate. They may give one of the amounts approximately but will fail for the other, so they cannot be the correct principal. Only Rs. 5400 satisfies both conditions exactly.

Common Pitfalls:

Learners sometimes try to guess the rate first by random trial, which wastes time. Another common error is to assume simple interest when the question clearly states compound interest. Recognizing that the ratio of successive amounts directly gives the growth factor is a key idea for solving such problems efficiently.

Final Answer:

The original sum invested is Rs. 5400.