Q.A machine presently worth ₹50,000 depreciates at 10% per annum. Using the GP concept, find its value after 3 years.

Depreciation at a fixed percentage per year is the mirror image of compound interest — the value each year is multiplied by $(1-d)$, forming a GP with common ratio less than 1.

Given: Present value $V_0 = ₹50{,}000$, depreciation rate $d = 10\% = 0.10$ per annum, $n = 3$ years.

Step 1 — Recognise the GP: year-end values form a GP with $a = V_0 = 50000$ and common ratio $r = (1-d) = 0.90$ (each year's value is 90% of the previous year's).

Step 2 — Apply the formula: $V_n = V_0(1-d)^n = 50000 \times (0.90)^3$.

Step 3 — Compute $(0.90)^3$: $(0.90)^2 = 0.81$; $(0.90)^3 = 0.81 \times 0.90 = 0.729$.

Step 4 — Multiply: $V_3 = 50000 \times 0.729 = 36450$. …

Subtracting the depreciation amount from the ORIGINAL value each year (₹50,000 − 3×₹5,000 = ₹35,000, a straight-line method) instead of applying the fixed PERCENTAGE to the reducing balance each year — a question saying 'depreciates at x% …