The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago. If its present value is Rs 291600. for how much it purchased?

Answer

To find the purchase price of the machine, we can use the formula for depreciation. The present value (PV) of an asset after depreciation can be calculated using the formula:

\[ PV = P \times \left(1 - \frac{R}{100}\right)^T \]

Where:
- \( PV \) = Present Value (Rs. 291600)
- \( P \) = Principal or Purchase Price (what we need to find)
- \( R \) = Rate of depreciation (10%)
- \( T \) = Time in years (3 years)

### Step 1: Write down the formula for present value after depreciation
We start with the formula:

\[ PV = P \times \left(1 - \frac{R}{100}\right)^T \]

### Step 2: Substitute the known values into the formula
Substituting the known values into the formula:

\[ 291600 = P \times \left(1 - \frac{10}{100}\right)^3 \]

### Step 3: Simplify the expression inside the parentheses
Calculate \( 1 - \frac{10}{100} \):

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

So now our equation becomes:

\[ 291600 = P \times (0.9)^3 \]

### Step 4: Calculate \( (0.9)^3 \)
Now calculate \( (0.9)^3 \):

\[ (0.9)^3 = 0.9 \times 0.9 \times 0.9 = 0.729 \]

Now the equation is:

\[ 291600 = P \times 0.729 \]

### Step 5: Solve for \( P \)
To find \( P \), divide both sides by \( 0.729 \):

\[ P = \frac{291600}{0.729} \]

### Step 6: Perform the division
Now calculate the division:

\[ P = 400000 \]

### Conclusion
The purchase price of the machine was Rs. 400000.

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