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

Options

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

Answer

To find the original purchase price of the bike, we can follow these steps:

### Step 1: Understand the depreciation
The bike depreciates at a rate of 10% per annum. This means that each year, the value of the bike is reduced by 10% of its value at the beginning of that year.

### Step 2: Define the variables
Let the original purchase price of the bike two years ago be denoted as \( x \).

### Step 3: Calculate the value after one year
After one year, the value of the bike will be:
\[ \text{Value after 1 year} = x - 0.10x = 0.90x = \frac{9}{10}x \]

### Step 4: Calculate the value after two years
After the second year, the value of the bike will again depreciate by 10%. Thus, the value after two years will be:
\[ \text{Value after 2 years} = \frac{9}{10}x - 0.10 \left(\frac{9}{10}x\right) = \frac{9}{10}x - \frac{9}{100}x = \frac{90}{100}x - \frac{9}{100}x = \frac{81}{100}x \]

### Step 5: Set up the equation
We know that the present value of the bike is Rs. 24,300. Therefore, we can set up the equation:
\[ \frac{81}{100}x = 24300 \]

### Step 6: Solve for \( x \)
To find \( x \), we can multiply both sides by \( \frac{100}{81} \):
\[ x = 24300 \times \frac{100}{81} \]

### Step 7: Calculate the value
Now we perform the multiplication:
\[ x = 24300 \times \frac{100}{81} = 24300 \times 1.2345679 \approx 30000 \]

### Final answer
Thus, the original purchase price of the bike was Rs. 30,000.

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