The value of a fixed asset depreciates at the rate of 10% of the value at the beginning of each year. If the value of the asset, two years ago, was ₹ 12000 more than the value of the asset one year ago, then find the present value of the asset, given that the asset was bought two years ago.

### Concept & Logic This problem elegantly tests your understanding of what depreciation actually means year-over-year. The difference in value between any consecutive years is exactly equal to the depreciation amount for that specific year. Since the rate is applied to the value at the *beginning* of the year, the drop in value during the first year is simply the depreciation percentage applied to the initial purchase price. ### Step-by-Step Solution * **Define the Timeline:** * 2 years ago: Year 0 (Initial Purchase Price) * 1 year ago: Year 1 (After 1st depreciation) * Present: Year 2 (After 2nd depreciation) * **Analyze the Given Difference:** We are given that the difference between the value 2 years ago (Year 0) and 1 year ago (Year 1) is ₹ 12000. This difference is precisely the depreciation amount for the first year. * **Calculate Initial Value:** The first year's depreciation is $10\%$ of the initial value. $$ 10\% \text{ of Initial Value} = 12000 $$ $$ \text{Initial Value} = 12000 \times 10 = 120000 $$ * **Calculate Present Value (Year 2):** The asset depreciates at $10\%$ successively for 2 years. The fractional multiplier for a $10\%$ decrease is $0.9$. $$ \text{Present Value} = \text{Initial Value} \times (0.9)^2 $$ $$ \text{Present Value} = 120000 \times 0.81 $$ $$ \text{Present Value} = 97200 $$ ### Exam Strategy & Shortcut **Direct Percentage Mapping:** You don't need algebra for this. Read the phrase: "value two years ago was ₹ 12000 more than... one year ago". This immediately translates to "First year drop = 12000". Since the drop is $10\%$, the base is instantly $120,000$. To find the value after 2 years of $10\%$ drops, multiply by $0.81$ ($90\%$ of $90\%$). $12 \times 81 = 972$. Add the zeroes to get $97200$. This can be solved entirely mentally in 15 seconds. ### Common Pitfall Students often set up unnecessarily complex quadratic or algebraic equations, defining the final value as $x$ and working backwards through multiple steps. By recognizing that the absolute difference between Year 0 and Year 1 is just the simple interest of the first year, you bypass the complex algebra entirely. ### Final Answer **Therefore, the correct answer is ₹ 97200.**