Depreciation applicable to an equipment is 20%. The value of the equipment 3 years from now will be less by

### Concept & Formula This problem asks for the total effective percentage decrease over 3 years. This requires applying the successive percentage change concept on an assumed base value. For an annual depreciation rate $R$, the remaining value after $n$ years is calculated as: $$ \text{Final Value} = \text{Initial Value} \times \left(1 - \frac{R}{100}\right)^n $$ ### Step-by-Step Solution * **Assume Initial Value:** Let the current value of the equipment be $100$. * **Depreciation Rate:** $20\%$ per year. * **Fractional Multiplier:** $100\% - 20\% = 80\%$. As a fraction, this is $\frac{80}{100} = \frac{4}{5}$ or $0.8$. * **Calculate Final Value after 3 years:** $$ \text{Final Value} = 100 \times 0.8 \times 0.8 \times 0.8 $$ $$ \text{Final Value} = 100 \times 0.512 = 51.2 $$ * **Calculate the Total Depreciation:** The question asks how much the value will be *less by*. $$ \text{Total Reduction} = \text{Initial Value} - \text{Final Value} $$ $$ \text{Total Reduction} = 100 - 51.2 = 48.8 $$ * Since our base was $100$, this reduction is directly $48.8\%$. ### Exam Strategy & Shortcut **Effective Percentage Formula (for 3 successive changes):** Alternatively, remember the cube of the multiplier. A $20\%$ decrease means the value is multiplied by $0.8$ each year. $0.8^3 = 0.512$. This means $51.2\%$ of the value remains. The depreciation is simply $100\% - 51.2\% = 48.8\%$. Knowing your cubes (like $8^3 = 512$) makes this a 5-second mental math problem. ### Common Pitfall The single most common mistake is choosing **51.2%**. Students correctly calculate the final remaining value ($51.2\%$) but fail to read the exact wording of the question: "will be less by". You must subtract the remaining value from the original $100\%$ to find the actual depreciation amount. ### Final Answer **Therefore, the correct answer is 48.8%.**