A man sold two articles at Rs 25920 each. These were sold at 8% gain and 4% loss respectively. Find the gain or loss percent in the whole transaction.

Answer

To solve the problem step by step, we will calculate the cost price of each article, the total profit or loss, and finally the overall gain or loss percentage.

### Step 1: Identify the Selling Price (SP) of each article
The selling price of each article is given as Rs 25,920.

### Step 2: Calculate the Cost Price (CP) of the first article
The first article is sold at an 8% gain. We can use the formula for cost price when there is a gain:
\[ CP_1 = \frac{100}{100 + \text{Gain Percent}} \times SP \]
Substituting the values:
\[ CP_1 = \frac{100}{100 + 8} \times 25920 = \frac{100}{108} \times 25920 \]
Calculating this:
\[ CP_1 = \frac{100 \times 25920}{108} = \frac{2592000}{108} = 24000 \]
So, the cost price of the first article is Rs 24,000.

### Step 3: Calculate the Cost Price (CP) of the second article
The second article is sold at a 4% loss. We can use the formula for cost price when there is a loss:
\[ CP_2 = \frac{100}{100 - \text{Loss Percent}} \times SP \]
Substituting the values:
\[ CP_2 = \frac{100}{100 - 4} \times 25920 = \frac{100}{96} \times 25920 \]
Calculating this:
\[ CP_2 = \frac{100 \times 25920}{96} = \frac{2592000}{96} = 27000 \]
So, the cost price of the second article is Rs 27,000.

### Step 4: Calculate the total cost price (TCP)
Now, we add the cost prices of both articles:
\[ TCP = CP_1 + CP_2 = 24000 + 27000 = 51000 \]

### Step 5: Calculate the total selling price (TSP)
The total selling price is:
\[ TSP = SP_1 + SP_2 = 25920 + 25920 = 51840 \]

### Step 6: Calculate the total profit or loss
Now, we find the total profit:
\[ \text{Total Profit} = TSP - TCP = 51840 - 51000 = 840 \]

### Step 7: Calculate the profit percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Total Profit}}{\text{Total Cost Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{840}{51000}\right) \times 100 \]
Calculating this:
\[ \text{Profit Percentage} = \frac{84000}{51000} \approx 1.647 \% \]

### Final Answer
The overall gain percentage in the whole transaction is approximately **1.65%**.

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