`60%` goods are sold at `5%` loss while rest are sold at `10%` profit. If there is a total profit of ₹ 100, then the worth of goods sold is:

Options

A. ₹ 6000
B. ₹ 5000
C. ₹ 10000
D. none of these

Answer

To solve the problem step by step, we need to analyze the given information about the goods sold at different profit and loss percentages.

### Step 1: Understand the distribution of goods
We know that 60% of the goods are sold at a 5% loss, and the remaining 40% are sold at a 10% profit.

### Step 2: Assign a value to the total worth of goods
Let the total worth of the goods be \( x \).

### Step 3: Calculate the worth of goods sold at a loss
The worth of goods sold at a 5% loss (60% of total goods):
\[ \text{Worth of goods sold at loss} = 0.6x \]
The selling price of these goods (since they are sold at a 5% loss):
\[ \text{Selling Price (SP) at loss} = \text{Cost Price (CP)} - \text{Loss} = 0.6x - 0.05(0.6x) = 0.6x - 0.03x = 0.57x \]

### Step 4: Calculate the worth of goods sold at a profit
The worth of goods sold at a 10% profit (40% of total goods):
\[ \text{Worth of goods sold at profit} = 0.4x \]
The selling price of these goods (since they are sold at a 10% profit):
\[ \text{Selling Price (SP) at profit} = \text{Cost Price (CP)} + \text{Profit} = 0.4x + 0.1(0.4x) = 0.4x + 0.04x = 0.44x \]

### Step 5: Calculate the total selling price
Now, we can calculate the total selling price of all goods:
\[ \text{Total Selling Price} = \text{SP at loss} + \text{SP at profit} = 0.57x + 0.44x = 1.01x \]

### Step 6: Relate total selling price to total profit
We know that the total profit is ₹100. The profit can also be calculated as:
\[ \text{Total Profit} = \text{Total Selling Price} - \text{Total Cost Price} = 1.01x - x = 0.01x \]
Setting this equal to the total profit:
\[ 0.01x = 100 \]

### Step 7: Solve for x
To find \( x \):
\[ x = \frac{100}{0.01} = 10000 \]

### Conclusion
The worth of the goods sold is ₹10,000.

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