The cost of a car, purchased 2 years ago depreciates at the rate of 20% per year. If its present value in 3,15,600, find :
Its value , when it was purchased 2 years ago.

Answer

To find the value of the car when it was purchased 2 years ago, we can use the formula for depreciation. The formula is:

\[ \text{Present Value} = \text{Original Value} \times \left(1 - \frac{\text{Rate}}{100}\right)^n \]

Where:
- Present Value = 3,15,600
- Rate = 20%
- n = 2 years

### Step 1: Set up the equation

We know the present value and we need to find the original value (let's denote it as \( A \)). Plugging in the known values into the formula gives us:

\[ 3,15,600 = A \times \left(1 - \frac{20}{100}\right)^2 \]

### Step 2: Simplify the equation

Calculate \( 1 - \frac{20}{100} \):

\[ 1 - \frac{20}{100} = 1 - 0.2 = 0.8 \]

Now, substitute this back into the equation:

\[ 3,15,600 = A \times (0.8)^2 \]

### Step 3: Calculate \( (0.8)^2 \)

\[ (0.8)^2 = 0.64 \]

Now the equation becomes:

\[ 3,15,600 = A \times 0.64 \]

### Step 4: Solve for \( A \)

To find \( A \), divide both sides by 0.64:

\[ A = \frac{3,15,600}{0.64} \]

### Step 5: Perform the division

Calculating the division:

\[ A = 4,93,750 \]

### Final Answer

The value of the car when it was purchased 2 years ago is **4,93,750**.

---