The value of a bike which was purchased 2 yr ago, depreciates at 10% per annum. If its present value is ₹ 24300. For how much was it purchased?

Options

A. ₹ 31000
B. ₹ 31500
C. ₹ 30000
D. ₹ 30550

Answer

To find the original purchase price of the bike, we can use the formula for depreciation. The value of an asset after depreciation can be calculated using the formula:

\[ \text{Present Value} = \text{Original Value} \times (1 - \text{Depreciation Rate})^{\text{Number of Years}} \]

Given:
- Present Value = ₹ 24300
- Depreciation Rate = 10% = 0.10
- Number of Years = 2

Let the original value (purchase price) be \( x \).

### Step 1: Set up the equation
Using the formula, we can set up the equation:

\[ 24300 = x \times (1 - 0.10)^2 \]

### Step 2: Simplify the equation
Calculate \( (1 - 0.10)^2 \):

\[ (1 - 0.10) = 0.90 \]
\[ (0.90)^2 = 0.81 \]

Now substitute this back into the equation:

\[ 24300 = x \times 0.81 \]

### Step 3: Solve for \( x \)
To find \( x \), divide both sides by 0.81:

\[ x = \frac{24300}{0.81} \]

### Step 4: Calculate the value
Now, perform the division:

\[ x = 30000 \]

### Conclusion
The original purchase price of the bike was ₹ 30000.