Ahmed buys a plot of land for Rs. 480000. He sells `2/5` of it at a loss of 6%.At what gain per cent should he sell the remaining part of the plot to gain 10% on the whole?

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total cost price of the plot
The cost price (CP) of the plot is given as Rs. 480,000.

### Step 2: Determine the portion of the plot sold
Ahmed sells \( \frac{2}{5} \) of the plot.

### Step 3: Calculate the cost price of the portion sold
The cost price of the portion sold is:
\[ \text{CP of portion sold} = \frac{2}{5} \times 480,000 = 192,000 \]

### Step 4: Calculate the selling price of the portion sold at a loss of 6%
To find the selling price (SP) at a loss of 6%, we use the formula:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Where Loss = 6% of CP.
\[ \text{Loss} = 6\% \text{ of } 192,000 = \frac{6}{100} \times 192,000 = 11,520 \]
Thus,
\[ \text{SP} = 192,000 - 11,520 = 180,480 \]

### Step 5: Calculate the total selling price needed for a 10% gain on the whole plot
To find the total selling price for a 10% gain on the entire plot, we calculate:
\[ \text{Total SP for 10% gain} = \text{CP} + \text{Gain} \]
Where Gain = 10% of CP.
\[ \text{Gain} = 10\% \text{ of } 480,000 = \frac{10}{100} \times 480,000 = 48,000 \]
Thus,
\[ \text{Total SP} = 480,000 + 48,000 = 528,000 \]

### Step 6: Calculate the selling price required for the remaining part of the plot
The selling price of the remaining part of the plot is:
\[ \text{SP of remaining part} = \text{Total SP} - \text{SP of portion sold} \]
\[ \text{SP of remaining part} = 528,000 - 180,480 = 347,520 \]

### Step 7: Calculate the cost price of the remaining part of the plot
The cost price of the remaining part is:
\[ \text{CP of remaining part} = \text{Total CP} - \text{CP of portion sold} \]
\[ \text{CP of remaining part} = 480,000 - 192,000 = 288,000 \]

### Step 8: Calculate the gain on the remaining part
Gain can be calculated as:
\[ \text{Gain} = \text{SP of remaining part} - \text{CP of remaining part} \]
\[ \text{Gain} = 347,520 - 288,000 = 59,520 \]

### Step 9: Calculate the gain percent for the remaining part
Gain percent is calculated using the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
\[ \text{Gain Percent} = \left( \frac{59,520}{288,000} \right) \times 100 \approx 20.69\% \]

### Final Answer
Ahmed should sell the remaining part of the plot at approximately **20.69% gain**.

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