Question

The value of a machine depreciates every year at the rate of 10% on its value at the beginning of that year. If the present value of the machine is Rs. 729, its worth three years ago was:

• A. Rs. 947.70
• B. Rs. 1,000
• C. Rs. 750.87
• D. Rs. 800

Hint:

To calculate the initial value of an asset with depreciation, use the formula \( \text{Initial Value} = \frac{\text{Final Value}}{(1 - \text{Depreciation Rate})^n} \).

Answer 1

The Correct Option is B

The machine depreciates 10% every year, meaning its value is reduced by 90% each year. The formula for depreciation is:
\[ \text{Value after } n \text{ years} = \text{Initial value} \times (0.9)^n \] Let the initial value be \( x \). After 3 years, the value of the machine becomes 729, so: \[ x \times (0.9)^3 = 729 \] \[ x \times 0.729 = 729 \] \[ x = \frac{729}{0.729} = 1,000 \] - Option (A) Rs. 947.70: This is incorrect, as it does not fit with the given depreciation rate.
- Option (C) Rs. 750.87: This is incorrect, as it does not match the calculation.
- Option (D) Rs. 800: This is also incorrect.