A man buys a field of agricultural land for 3,60,000. He sells one-third at a loss of 20% and `2/5` th at a gain of 25%. At what price must he sell the remaining 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 will break down the transactions and calculate the necessary values.

### Step 1: Calculate the total cost of the field.
The man buys the field for ₹3,60,000.

### Step 2: Calculate the total selling price needed for a 10% profit.
To find out the total selling price needed for a 10% profit, we calculate:
\[ \text{Total Selling Price} = \text{Cost Price} + \text{Profit} \]
\[ \text{Profit} = 10\% \text{ of } 3,60,000 = \frac{10}{100} \times 3,60,000 = 36,000 \]
\[ \text{Total Selling Price} = 3,60,000 + 36,000 = 3,96,000 \]

### Step 3: Calculate the amount sold in the first transaction (one-third at a loss of 20%).
The man sells one-third of the field:
\[ \text{Area sold} = \frac{1}{3} \text{ of total area} \]
\[ \text{Cost of one-third} = \frac{1}{3} \times 3,60,000 = 1,20,000 \]
He sells it at a loss of 20%, so the selling price for this portion is:
\[ \text{Selling Price} = \text{Cost} - \text{Loss} \]
\[ \text{Loss} = 20\% \text{ of } 1,20,000 = \frac{20}{100} \times 1,20,000 = 24,000 \]
\[ \text{Selling Price} = 1,20,000 - 24,000 = 96,000 \]

### Step 4: Calculate the amount sold in the second transaction (two-fifths at a gain of 25%).
The man sells two-fifths of the field:
\[ \text{Area sold} = \frac{2}{5} \text{ of total area} \]
\[ \text{Cost of two-fifths} = \frac{2}{5} \times 3,60,000 = 1,44,000 \]
He sells it at a gain of 25%, so the selling price for this portion is:
\[ \text{Selling Price} = \text{Cost} + \text{Gain} \]
\[ \text{Gain} = 25\% \text{ of } 1,44,000 = \frac{25}{100} \times 1,44,000 = 36,000 \]
\[ \text{Selling Price} = 1,44,000 + 36,000 = 1,80,000 \]

### Step 5: Calculate the total selling price from the first two transactions.
\[ \text{Total Selling Price from first two transactions} = 96,000 + 1,80,000 = 2,76,000 \]

### Step 6: Calculate the selling price required for the remaining field.
To find out how much he needs to sell the remaining field for, we subtract the total selling price from the total selling price needed for a 10% profit:
\[ \text{Required Selling Price for remaining field} = \text{Total Selling Price} - \text{Total Selling Price from first two transactions} \]
\[ \text{Required Selling Price for remaining field} = 3,96,000 - 2,76,000 = 1,20,000 \]

### Final Answer:
The man must sell the remaining field for ₹1,20,000 to achieve an overall profit of 10%.

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