Two friends bought one flat and one land in 2 lakh and 2 lakh 20 thousand respectively. Flat and land increase at a rate of `20%` and `10%` per annum respectively. Then they exchange their assets after 2 years, then find the profit percet of the person who got profit ?

Options

A. `6.2%`
B. `8.2%`
C. `5.8%`
D. `8.5%`

Answer

To solve the problem step by step, we need to calculate the value of the flat and the land after 2 years, and then determine the profit percentage for the person who gains from the exchange.

### Step 1: Calculate the future value of the flat after 2 years.
- **Initial value of the flat** = ₹2,00,000
- **Rate of increase** = 20% per annum
- **Future Value (FV) formula**:
\[ FV = P(1 + r)^n \]
where \( P \) is the principal amount, \( r \) is the rate of interest, and \( n \) is the number of years.

- Plugging in the values:
\[ FV_{flat} = 2,00,000 \times (1 + 0.20)^2 \]
\[ FV_{flat} = 2,00,000 \times (1.20)^2 \]
\[ FV_{flat} = 2,00,000 \times 1.44 = 2,88,000 \]

### Step 2: Calculate the future value of the land after 2 years.
- **Initial value of the land** = ₹2,20,000
- **Rate of increase** = 10% per annum

- Plugging in the values:
\[ FV_{land} = 2,20,000 \times (1 + 0.10)^2 \]
\[ FV_{land} = 2,20,000 \times (1.10)^2 \]
\[ FV_{land} = 2,20,000 \times 1.21 = 2,66,200 \]

### Step 3: Determine who made a profit after the exchange.
- After 2 years, the flat is worth ₹2,88,000 and the land is worth ₹2,66,200.
- The person who received the flat gained more value compared to the person who received the land.

### Step 4: Calculate the profit made by the person who received the flat.
- **Profit** = Value of flat - Value of land
\[ Profit = 2,88,000 - 2,66,200 = 21,800 \]

### Step 5: Calculate the profit percentage.
- **Profit Percentage formula**:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
- Here, the cost price is the initial value of the flat, which is ₹2,00,000.
\[ \text{Profit Percentage} = \left( \frac{21,800}{2,00,000} \right) \times 100 \]
\[ \text{Profit Percentage} = 0.109 \times 100 = 10.9\% \]

### Final Answer:
The profit percentage of the person who got profit is approximately **10.9%**.

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