The price of motor cycle depreciates every year by 10%. If the value of the motor cycle after 3 years will be Rs. 36450, then what is the present value (in Rs.) of the motor cycle?

Options

A. 45000
B. 50000
C. 48000
D. 51000

Answer

To find the present value of the motorcycle given that it depreciates by 10% each year and its value after 3 years is Rs. 36,450, we can use the formula for depreciation:

### Step-by-Step Solution:

1. **Identify the variables:**
- Let \( P \) be the present value of the motorcycle.
- The depreciation rate \( r = 10\% \).
- The final value after 3 years \( A = 36,450 \).
- The time period \( t = 3 \) years.

2. **Write the formula for depreciation:**
The formula for the final value after depreciation is given by:
\[ A = P \times \left(1 - \frac{r}{100}\right)^t \]
Substituting the known values:
\[ 36,450 = P \times \left(1 - \frac{10}{100}\right)^3 \]

3. **Calculate \( 1 - \frac{r}{100} \):**
\[ 1 - \frac{10}{100} = 1 - 0.1 = 0.9 \]

4. **Substitute this value into the equation:**
\[ 36,450 = P \times (0.9)^3 \]

5. **Calculate \( (0.9)^3 \):**
\[ (0.9)^3 = 0.729 \]
So, the equation becomes:
\[ 36,450 = P \times 0.729 \]

6. **Rearrange the equation to solve for \( P \):**
\[ P = \frac{36,450}{0.729} \]

7. **Calculate \( P \):**
\[ P = \frac{36,450 \times 1000}{729} \quad (\text{Multiplying numerator and denominator by } 1000) \]
\[ P = \frac{36,450,000}{729} \approx 50,000 \]

### Conclusion:
The present value of the motorcycle is approximately Rs. 50,000.