Machine Value: Overall Percentage Change Calculation

This solution explains how to find the overall percentage change in a machine's value after a sequence of depreciation and appreciation steps.

Step-by-Step Solution

Let the initial value of the machine be represented by $V$. We will track the changes step-by-step.

1. First Depreciation (20%): The value decreases by 20%. The new value is calculated as: $ V_1 = V \times (1 - \frac{20}{100}) = V \times (1 - 0.20) = 0.80V $
2. Appreciation (25%): The current value ($V_1$) increases by 25%. The new value is calculated as: $ V_2 = V_1 \times (1 + \frac{25}{100}) = 0.80V \times (1 + 0.25) = 0.80V \times 1.25 = 1.00V $
3. Final Depreciation (10%): The current value ($V_2$) decreases by 10%. The final value is calculated as: $ V_3 = V_2 \times (1 - \frac{10}{100}) = 1.00V \times (1 - 0.10) = 1.00V \times 0.90 = 0.90V $

Overall Percentage Change Analysis

To find the overall percentage change, compare the final value ($V_3 = 0.90V$) to the initial value ($V$).

• Change in value = Final Value - Initial Value = $0.90V - V = -0.10V$.
• The negative sign indicates a decrease in value.
• The formula for percentage change is: $ \text{Percentage Change} = \left( \frac{\text{Change in Value}}{\text{Initial Value}} \right) \times 100\% $
• Substituting the values: $ \text{Percentage Change} = \left( \frac{-0.10V}{V} \right) \times 100\% = -0.10 \times 100\% = -10\% $

The overall change in the machine's value is a 10% decrease.