Reverse depreciation — find value 3 years ago at 10% yearly drop: A machine depreciates at 10% each year on its beginning-of-year value. If its present value is ₹ 729, what was its worth 3 years ago?

Introduction / Context:
Depreciation at a fixed percentage each year is a compound decrease. To find the earlier value from a current value, divide by the compounded decay factor over the elapsed years.

Given Data / Assumptions:

• Current value V_now = ₹ 729
• Yearly depreciation = 10% → yearly multiplier = 0.90
• We need value 3 years ago (reverse 3 years of depreciation)

Concept / Approach:
Forward: V_now = V_past * (0.90)^3. Hence V_past = V_now / (0.90)^3. Since 0.9^3 = 0.729, this inversion is clean.

Step-by-Step Solution:
(0.90)^3 = 0.729V_past = 729 / 0.729 = ₹ 1000

Verification / Alternative check:
Apply depreciation forward: 1000 → 900 → 810 → 729 (exact).

Why Other Options Are Wrong:
₹ 947.10 or ₹ 750.87 are not exact reversals for 10% three times; ₹ 800 and ₹ 900 are intermediate-year values, not 3 years ago.

Common Pitfalls:
Subtracting 10% three times from the original instead of compounding multiplicatively, which would misestimate past value.

Final Answer:
₹ 1000