The value of a machine depreciates at the rate of 20% per annum. It was purchased 2 years ago. If its present value is Rs 40000, for hoe much was it purchased?

Options

A. Rs 56000
B. Rs 62500
C. Rs 65200
D. Rs 56500

Answer

To find the original purchase price of the machine, we will use the formula for depreciation. The present value (amount after depreciation) is given, and we need to find the principal (initial value).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Rate of depreciation (r) = 20% per annum
- Time (n) = 2 years
- Present value (A) = Rs 40,000

2. **Understand the Depreciation Formula:**
The formula for the present value after depreciation is:
\[ A = P \left(1 - \frac{r}{100}\right)^n \]
where:
- \( A \) = Present value
- \( P \) = Principal (initial value)
- \( r \) = Rate of depreciation
- \( n \) = Time in years

3. **Substitute the Known Values into the Formula:**
\[ 40,000 = P \left(1 - \frac{20}{100}\right)^2 \]
Simplifying the term inside the brackets:
\[ 1 - \frac{20}{100} = 1 - 0.2 = 0.8 \]
Therefore, the equation becomes:
\[ 40,000 = P (0.8)^2 \]

4. **Calculate \( (0.8)^2 \):**
\[ (0.8)^2 = 0.64 \]
Now the equation is:
\[ 40,000 = P \times 0.64 \]

5. **Solve for \( P \):**
To find \( P \), divide both sides by 0.64:
\[ P = \frac{40,000}{0.64} \]

6. **Calculate \( P \):**
\[ P = 62,500 \]

7. **Conclusion:**
Therefore, the initial purchase price of the machine was Rs 62,500.

### Summary of the Solution:
The original purchase price of the machine was Rs 62,500.

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