Variable Compound Rates — A sum is invested at 5%, 10%, and 20% successively for three years (compounded annually) and amounts to ₹ 16,632. Find the original principal.

Introduction / Context:
When annual rates vary year to year, the amount is the product of each year's growth factor times the principal.

Given Data / Assumptions:

• A = ₹ 16,632.
• Year-wise rates: 5%, then 10%, then 20%.

Concept / Approach:
Amount factor = 1.05 * 1.10 * 1.20 = 1.386. Thus A = P * 1.386.

Step-by-Step Solution:
P = 16,632 / 1.386 = ₹ 12,000

Verification / Alternative check:
12,000 * 1.386 = 16,632 exactly.

Why Other Options Are Wrong:
They do not match the precise division by 1.386.

Common Pitfalls:
Adding rates instead of multiplying annual growth factors.

Final Answer:
₹ 12,000