A man sold two chairs for Rs. 500 each. On one he gains 20% and on the other he loses 12% His net gain or loss per cent is

Options

A. 1.5% gain
B. 2% gain
C. 1.5% loss
D. 2% loss

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Selling Prices
The man sold two chairs for Rs. 500 each. Therefore, the selling price (SP) of each chair is:
- SP of Chair 1 = Rs. 500
- SP of Chair 2 = Rs. 500

### Step 2: Calculate the Cost Price of Chair 1
Chair 1 has a gain of 20%.
Let the cost price (CP) of Chair 1 be CP1.

Since the selling price is 120% of the cost price (100% + 20% gain), we can write:
\[ SP_1 = 120\% \text{ of } CP_1 \]
\[ 500 = \frac{120}{100} \times CP_1 \]

Now, rearranging to find CP1:
\[ CP_1 = 500 \times \frac{100}{120} \]
\[ CP_1 = 500 \times \frac{5}{6} \]
\[ CP_1 = 416.67 \text{ (approximately)} \]

### Step 3: Calculate the Cost Price of Chair 2
Chair 2 has a loss of 12%.
Let the cost price of Chair 2 be CP2.

Since the selling price is 88% of the cost price (100% - 12% loss), we can write:
\[ SP_2 = 88\% \text{ of } CP_2 \]
\[ 500 = \frac{88}{100} \times CP_2 \]

Now, rearranging to find CP2:
\[ CP_2 = 500 \times \frac{100}{88} \]
\[ CP_2 = 500 \times \frac{25}{22} \]
\[ CP_2 = 568.18 \text{ (approximately)} \]

### Step 4: Calculate Total Cost Price
Now, we can find the total cost price (CP_total):
\[ CP_{\text{total}} = CP_1 + CP_2 \]
\[ CP_{\text{total}} = 416.67 + 568.18 \]
\[ CP_{\text{total}} = 984.85 \text{ (approximately)} \]

### Step 5: Calculate Total Selling Price
The total selling price (SP_total) is:
\[ SP_{\text{total}} = SP_1 + SP_2 \]
\[ SP_{\text{total}} = 500 + 500 \]
\[ SP_{\text{total}} = 1000 \]

### Step 6: Calculate Profit
Now, we can calculate the profit:
\[ \text{Profit} = SP_{\text{total}} - CP_{\text{total}} \]
\[ \text{Profit} = 1000 - 984.85 \]
\[ \text{Profit} = 15.15 \text{ (approximately)} \]

### Step 7: Calculate Profit Percentage
Finally, we can calculate the profit percentage:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP_{\text{total}}} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{15.15}{984.85} \right) \times 100 \]
\[ \text{Profit Percentage} \approx 1.54\% \]

### Conclusion
The net gain percentage is approximately **1.54%**.

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