A man sold 280 chairs and had a gain equal to selling price of 35 chairs. What is his profit percentage ?

Options

A. 0.2
B. 0.1428
C. 0.15
D. 0.1667

Answer

To find the profit percentage from the given problem, we can follow these steps:

### Step-by-Step Solution:

1. **Assume Selling Price of One Chair**:
Let's assume the selling price (SP) of one chair is ₹100. This simplifies our calculations.

**Hint**: When calculating percentages, it's often easier to assume a base value (like ₹100) for simplicity.

2. **Calculate Total Selling Price**:
The man sold 280 chairs. Therefore, the total selling price (TSP) can be calculated as:
\[ \text{TSP} = \text{Number of Chairs} \times \text{SP of One Chair} = 280 \times 100 = ₹28000 \]

**Hint**: Always multiply the quantity by the unit price to find the total price.

3. **Calculate Profit**:
The profit is equal to the selling price of 35 chairs. Therefore, the profit (P) can be calculated as:
\[ P = 35 \times 100 = ₹3500 \]

**Hint**: Profit can often be calculated by determining the selling price of the items that contributed to the profit.

4. **Calculate Cost Price**:
The cost price (CP) can be found using the formula:
\[ \text{CP} = \text{TSP} - \text{Profit} = 28000 - 3500 = ₹24500 \]

**Hint**: The cost price can be found by subtracting the profit from the total selling price.

5. **Calculate Profit Percentage**:
The profit percentage (PP) is given by the formula:
\[ \text{PP} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{3500}{24500}\right) \times 100 \]
Simplifying this:
\[ \text{PP} = \left(\frac{3500 \times 100}{24500}\right) = \frac{350000}{24500} \approx 14.2857 \]
Rounding off, we get approximately 14.28%.

**Hint**: To find the profit percentage, always divide the profit by the cost price and multiply by 100.

### Final Answer:
The profit percentage is approximately **14.28%**.