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 depreciation:

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

Where:
- \( A \) is the present value (the value after depreciation),
- \( P \) is the principal amount (the original value),
- \( r \) is the rate of depreciation,
- \( n \) is the number of years.

Given:
- \( A = 97,200 \)
- \( r = 10\% \)
- \( n = 2 \)

### Step 1: Substitute the known values into the formula.

\[ 97,200 = P \left(1 - \frac{10}{100}\right)^2 \]

### Step 2: Simplify the expression inside the parentheses.

\[ 1 - \frac{10}{100} = 1 - 0.1 = 0.9 \]

So, we can rewrite the equation as:

\[ 97,200 = P (0.9)^2 \]

### Step 3: Calculate \( (0.9)^2 \).

\[ (0.9)^2 = 0.81 \]

Now the equation becomes:

\[ 97,200 = P \cdot 0.81 \]

### Step 4: Solve for \( P \).

To find \( P \), divide both sides by \( 0.81 \):

\[ P = \frac{97,200}{0.81} \]

### Step 5: Calculate the value of \( P \).

\[ P = 120,000 \]

### Final Answer:

The original value of the machine when it was purchased was Rs 120,000.

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