Amol bought a plot of land for 70,000 and a car for 32,000 on the same day. The value of the plot appreciates uniformly at the rate of 10% every year while the value of the car depreciates by 20% for the first year and by 10% for the second year. If Amol sells the plot of land as well as the car after 2 years, what will be the profit or loss on the whole ?

Answer

To find the profit or loss Amol incurred after selling the plot of land and the car, we will follow these steps:

### Step 1: Calculate the value of the plot of land after 2 years.
- The initial value of the plot of land = ₹70,000.
- The rate of appreciation = 10% per year.

Using the formula for appreciation:
\[ \text{Value after 2 years} = \text{Initial Value} \times \left(1 + \frac{R}{100}\right)^n \]
where \( R \) is the rate of appreciation and \( n \) is the number of years.

Substituting the values:
\[ \text{Value after 2 years} = 70,000 \times \left(1 + \frac{10}{100}\right)^2 \]
\[ = 70,000 \times \left(1.1\right)^2 \]
\[ = 70,000 \times 1.21 = 84,700 \]

### Step 2: Calculate the value of the car after 2 years.
- The initial value of the car = ₹32,000.
- The car depreciates by 20% in the first year and by 10% in the second year.

Calculating the value after the first year:
\[ \text{Value after 1st year} = \text{Initial Value} \times \left(1 - \frac{20}{100}\right) \]
\[ = 32,000 \times 0.8 = 25,600 \]

Calculating the value after the second year:
\[ \text{Value after 2nd year} = \text{Value after 1st year} \times \left(1 - \frac{10}{100}\right) \]
\[ = 25,600 \times 0.9 = 23,040 \]

### Step 3: Calculate the total selling price.
Now, we add the values of the plot of land and the car:
\[ \text{Total Selling Price} = \text{Value of Plot} + \text{Value of Car} \]
\[ = 84,700 + 23,040 = 107,740 \]

### Step 4: Calculate the total cost price.
The total cost price is the sum of the initial costs of the plot and the car:
\[ \text{Total Cost Price} = \text{Cost of Plot} + \text{Cost of Car} \]
\[ = 70,000 + 32,000 = 102,000 \]

### Step 5: Calculate profit or loss.
Now, we find the profit or loss by subtracting the total cost price from the total selling price:
\[ \text{Profit or Loss} = \text{Total Selling Price} - \text{Total Cost Price} \]
\[ = 107,740 - 102,000 = 5,740 \]

### Conclusion:
Amol made a profit of ₹5,740 after selling the plot of land and the car.

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