The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is ₹ 8748, its purchase price was

Options

A. ₹ `10000`
B. ₹ `11372`
C. ₹ `12000`
D. ₹ `12500`

Answer

To find the purchase price of the machine that depreciates at a rate of 10% per year and has a present value of ₹8748 after 3 years, we can use the formula for depreciation.

### Step-by-Step Solution:

1. **Understand the Depreciation Formula**:
The formula for the present value (PV) after depreciation is:
\[ PV = P \times (1 - r)^n \]
where:
- \( PV \) = Present Value
- \( P \) = Purchase Price (Principal)
- \( r \) = Rate of depreciation (as a decimal)
- \( n \) = Number of years

2. **Identify the Given Values**:
- Present Value \( PV = ₹8748 \)
- Rate of depreciation \( r = 10\% = 0.10 \)
- Number of years \( n = 3 \)

3. **Substitute the Values into the Formula**:
\[ 8748 = P \times (1 - 0.10)^3 \]
Simplifying further:
\[ 8748 = P \times (0.90)^3 \]

4. **Calculate \( (0.90)^3 \)**:
\[ (0.90)^3 = 0.729 \]
So the equation becomes:
\[ 8748 = P \times 0.729 \]

5. **Solve for \( P \)**:
To find \( P \), divide both sides by \( 0.729 \):
\[ P = \frac{8748}{0.729} \]

6. **Calculate the Purchase Price**:
Performing the division:
\[ P = 12000 \]

### Final Answer:
The purchase price of the machine was ₹12000.