The price of a car depreciates in the first year by 25% in the second year by 20% in the third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Rs. 10,00,000 :

Options

A. 7,80,000
B. 5,10,000
C. 6,90,000
D. 1,70,000

Answer

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

### Step 1: Calculate the depreciation for the first year.
- The initial cost of the car is Rs. 10,00,000.
- The depreciation in the first year is 25%.

**Calculation:**
1. Calculate 25% of Rs. 10,00,000:
\[ 25\% \text{ of } 10,00,000 = \frac{25}{100} \times 10,00,000 = 2,50,000 \]
2. Subtract the depreciation from the initial cost:
\[ \text{Price after 1st year} = 10,00,000 - 2,50,000 = 7,50,000 \]

### Step 2: Calculate the depreciation for the second year.
- The value of the car at the end of the first year is Rs. 7,50,000.
- The depreciation in the second year is 20%.

**Calculation:**
1. Calculate 20% of Rs. 7,50,000:
\[ 20\% \text{ of } 7,50,000 = \frac{20}{100} \times 7,50,000 = 1,50,000 \]
2. Subtract the depreciation from the value at the end of the first year:
\[ \text{Price after 2nd year} = 7,50,000 - 1,50,000 = 6,00,000 \]

### Step 3: Calculate the depreciation for the third year.
- The value of the car at the end of the second year is Rs. 6,00,000.
- The depreciation in the third year is 15%.

**Calculation:**
1. Calculate 15% of Rs. 6,00,000:
\[ 15\% \text{ of } 6,00,000 = \frac{15}{100} \times 6,00,000 = 90,000 \]
2. Subtract the depreciation from the value at the end of the second year:
\[ \text{Price after 3rd year} = 6,00,000 - 90,000 = 5,10,000 \]

### Final Price of the Car
The final price of the car after 3 years is Rs. 5,10,000.

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