The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago, and its present value is Rs. 8,748. What was the original purchase price of the machine?

Introduction / Context:
This is a depreciation percentage problem, where the value of an asset such as a machine decreases by a fixed percentage each year. The present value after a certain number of years is given, and we need to work backwards to find the original purchase price. Such questions are common in aptitude exams, finance, and accounting, and they test a clear understanding of successive percentage changes and reverse calculations.

Given Data / Assumptions:

• The machine depreciates at 10% per year.
• Number of years since purchase = 3 years.
• Present value after 3 years = Rs. 8,748.
• Let the original purchase price be P rupees.

Concept / Approach:
Depreciation at a fixed percentage means the value is multiplied each year by (1 - depreciation rate). Here, the depreciation rate is 10%, so each year the value is multiplied by 0.9. Over 3 years, the value is multiplied by 0.9 three times, that is by 0.9^3. Therefore, Present value = Original value * (0.9^3). To find the original value, we divide the present value by 0.9^3. This is an example of using the compound depreciation formula, which is similar in structure to compound interest but with a negative rate.

Step-by-Step Solution:
Step 1: Let the original purchase price be P. Step 2: Depreciation rate per year = 10%, so each year the value is multiplied by 0.9. Step 3: After 3 years, value factor = 0.9^3 = 0.9 * 0.9 * 0.9. Step 4: Compute 0.9^3 = 0.729. Step 5: Present value after 3 years = P * 0.729 = 8748. Step 6: Solve for P: P = 8748 / 0.729. Step 7: Perform the division: 8748 / 0.729 = 12000. Step 8: Therefore, the machine was originally purchased for Rs. 12,000.

Verification / Alternative check:
Forward check: Start from Rs. 12,000 and apply 10% depreciation each year. End of year 1: 12000 * 0.9 = 10800. End of year 2: 10800 * 0.9 = 9720. End of year 3: 9720 * 0.9 = 8748. This matches the given present value exactly, which verifies that Rs. 12,000 is correct.

Why Other Options Are Wrong:
Rs. 14,000, Rs. 12,800, and Rs. 15,000, when depreciated by 10% over 3 years, do not reduce to Rs. 8,748. For example, 14000 * 0.729 = 10206, which is too high, and 10000 * 0.729 = 7290, which is too low. Only Rs. 12,000 produces the exact present value. Therefore the other options are incorrect.

Common Pitfalls:
A common mistake is to subtract 10% of the original value three times without compounding, which treats depreciation as simple rather than compound. Another error is to divide by 0.9 instead of 0.9^3 when reversing three years of depreciation. Learners must remember that repeated percentage changes require powers of the multiplication factor, not linear subtraction or division by the rate only once.

Final Answer:
The original purchase price of the machine was Rs. 12,000.