A motorcycle is bought at Rs 160000. Its value depreciates at the rate of 10% per annum. Find its value after (i) 1 year ,(ii) 2 year.

Answer

To find the value of the motorcycle after 1 year and 2 years of depreciation at a rate of 10% per annum, we can follow these steps:

### Step 1: Identify the initial values
- **Principal Amount (P)**: Rs 160,000
- **Depreciation Rate (R)**: 10% per annum

### Step 2: Calculate the value after 1 year
The formula to calculate the depreciated value after 1 year is:
\[ \text{Value after 1 year} = P \times \left(1 - \frac{R}{100}\right) \]

Substituting the values:
\[ \text{Value after 1 year} = 160000 \times \left(1 - \frac{10}{100}\right) \]
\[ = 160000 \times \left(1 - 0.10\right) \]
\[ = 160000 \times 0.90 \]
\[ = 144000 \]

### Step 3: Calculate the value after 2 years
To find the value after 2 years, we can use the value after 1 year as the new principal:
\[ \text{Value after 2 years} = \text{Value after 1 year} \times \left(1 - \frac{R}{100}\right) \]

Substituting the values:
\[ \text{Value after 2 years} = 144000 \times \left(1 - \frac{10}{100}\right) \]
\[ = 144000 \times 0.90 \]
\[ = 129600 \]

### Final Answers:
- **Value after 1 year**: Rs 144,000
- **Value after 2 years**: Rs 129,600

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