A man buys a field of agricultur al land for 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the re maining field so as to make an overall profit of 10 % ?

Options

A. 1,00,000
B. 1,15,000
C. 1,20,000
D. 1,25,000

Answer

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

### Step 1: Calculate the Cost Price (CP)
The cost price of the agricultural land is given as:
\[ \text{CP} = 3,60,000 \]

### Step 2: Calculate the Overall Selling Price (SP) for 10% Profit
To find the overall selling price needed to achieve a 10% profit, we calculate:
\[ \text{Profit} = \text{CP} \times \frac{10}{100} = 3,60,000 \times 0.10 = 36,000 \]
Thus, the overall selling price (SP) is:
\[ \text{SP} = \text{CP} + \text{Profit} = 3,60,000 + 36,000 = 3,96,000 \]

### Step 3: Calculate Selling Price of One-Third of the Field at 20% Loss
One-third of the field is sold at a loss of 20%. The cost of one-third of the field is:
\[ \text{Cost of One-Third} = \frac{3,60,000}{3} = 1,20,000 \]
The selling price (SP) at a 20% loss is:
\[ \text{SP} = \text{Cost} \times (1 - \frac{20}{100}) = 1,20,000 \times 0.80 = 96,000 \]

### Step 4: Calculate Selling Price of Two-Fifths of the Field at 25% Gain
Two-fifths of the field is sold at a gain of 25%. The cost of two-fifths of the field is:
\[ \text{Cost of Two-Fifths} = \frac{3,60,000 \times 2}{5} = 1,44,000 \]
The selling price (SP) at a 25% gain is:
\[ \text{SP} = \text{Cost} \times (1 + \frac{25}{100}) = 1,44,000 \times 1.25 = 1,80,000 \]

### Step 5: Calculate Total Selling Price from Sold Portions
Now, we add the selling prices from the portions sold:
\[ \text{Total SP from Sold Portions} = 96,000 + 1,80,000 = 2,76,000 \]

### Step 6: Calculate the Selling Price Required for the Remaining Field
To find the selling price required for the remaining part of the field, we subtract the total selling price from the overall selling price:
\[ \text{Required SP for Remaining Field} = \text{Overall SP} - \text{Total SP from Sold Portions} \]
\[ = 3,96,000 - 2,76,000 = 1,20,000 \]

### Final Answer
The selling price at which he must sell the remaining field to achieve an overall profit of 10% is:
\[ \text{Required SP} = 1,20,000 \]

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