The value of a machine depreciates at the rate of 10% per year. It was purchased 3 yr ago. If its present value is ₹ 145800 for how much was it purchased?

Options

A. ₹ 175800
B. ₹ 180000
C. ₹ 200000
D. ₹ 210000

Answer

To find the original purchase price of the machine, we need to calculate its value before it depreciated over the past 3 years. The machine depreciates at a rate of 10% per year.

### Step-by-Step Solution:

1. **Understand the Depreciation Formula**:
The formula for depreciation is given by:
\[ \text{Present Value} = \text{Original Value} \times (1 - \text{Depreciation Rate})^n \]
where \( n \) is the number of years.

2. **Identify the Variables**:
- Present Value (PV) = ₹145800
- Depreciation Rate = 10% = 0.10
- Number of Years (n) = 3

3. **Set Up the Equation**:
We need to find the Original Value (OV). Plugging in the known values into the formula:
\[ 145800 = OV \times (1 - 0.10)^3 \]

4. **Calculate the Depreciation Factor**:
Calculate \( (1 - 0.10)^3 \):
\[ (1 - 0.10)^3 = (0.90)^3 = 0.729 \]

5. **Rewrite the Equation**:
Now the equation becomes:
\[ 145800 = OV \times 0.729 \]

6. **Solve for Original Value (OV)**:
Rearranging the equation to find OV:
\[ OV = \frac{145800}{0.729} \]

7. **Perform the Division**:
Calculate the value:
\[ OV = 200000 \]

### Conclusion:
The original purchase price of the machine was ₹200000.