The value of a machine, purchased two years ago, depreciates at the annual rate of 10%. If its present value is Rs 97,200, find its value when it was purchased.

Answer

To find the original value of the machine when it was purchased, we can use the formula for compound interest, which is also applicable for depreciation. The formula is:

\[ A = P \left(1 + \frac{r}{100}\right)^t \]

Where:
- \( A \) is the present value (current value of the machine),
- \( P \) is the principal amount (original value when purchased),
- \( r \) is the rate of depreciation,
- \( t \) is the time in years.

### Step-by-Step Solution:

1. **Identify the given values:**
- Present value \( A = 97,200 \) Rs
- Rate of depreciation \( r = -10\% \) (since it is depreciation, we consider it negative)
- Time \( t = 2 \) years

2. **Convert the rate of depreciation:**
- Since we are using the formula, we need to express the depreciation rate as a positive value for calculation:
\[ r = -10\% = -\frac{10}{100} = -0.10 \]

3. **Substitute the values into the formula:**
\[ 97,200 = P \left(1 - 0.10\right)^2 \]
This simplifies to:
\[ 97,200 = P \left(0.90\right)^2 \]

4. **Calculate \( (0.90)^2 \):**
\[ (0.90)^2 = 0.81 \]
So, we rewrite the equation:
\[ 97,200 = P \times 0.81 \]

5. **Solve for \( P \):**
\[ P = \frac{97,200}{0.81} \]

6. **Perform the division:**
\[ P = 120,000 \]

7. **Conclusion:**
The value of the machine when it was purchased was **Rs 120,000**.