A new car costs Rs 360000. Its price depreciates at the rate of 10% a year during the first two years and at the rate of 20% a year thereafter. What will be the price of the car after 3 years?

Options

A. 184,320
B. 171,456
C. 125,456
D. 147,456

Answer

To find the price of the car after 3 years, we will calculate the depreciation for each year step by step.

### Step 1: Calculate the price after the first year
The initial price of the car is Rs. 360,000. The depreciation rate for the first year is 10%.

1. **Calculate the depreciation amount for the first year:**
\[ \text{Depreciation for Year 1} = \text{Initial Price} \times \text{Depreciation Rate} = 360000 \times 0.10 = 36000 \]

2. **Calculate the price after the first year:**
\[ \text{Price after Year 1} = \text{Initial Price} - \text{Depreciation for Year 1} = 360000 - 36000 = 324000 \]

### Step 2: Calculate the price after the second year
The depreciation rate for the second year is also 10%.

1. **Calculate the depreciation amount for the second year:**
\[ \text{Depreciation for Year 2} = \text{Price after Year 1} \times \text{Depreciation Rate} = 324000 \times 0.10 = 32400 \]

2. **Calculate the price after the second year:**
\[ \text{Price after Year 2} = \text{Price after Year 1} - \text{Depreciation for Year 2} = 324000 - 32400 = 291600 \]

### Step 3: Calculate the price after the third year
The depreciation rate for the third year is 20%.

1. **Calculate the depreciation amount for the third year:**
\[ \text{Depreciation for Year 3} = \text{Price after Year 2} \times \text{Depreciation Rate} = 291600 \times 0.20 = 58320 \]

2. **Calculate the price after the third year:**
\[ \text{Price after Year 3} = \text{Price after Year 2} - \text{Depreciation for Year 3} = 291600 - 58320 = 233280 \]

### Final Answer
The price of the car after 3 years is Rs. 233,280.

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