By selling an article for 69, there is a loss of 8%, when the article is sold for 78, the gain or loss per cent is

Options

A. neither loss nor gain
B. 4%gain
C. 4%loss
D. 40%gain

Answer

To solve the problem step by step, we will first determine the cost price (CP) of the article based on the information given about the selling price (SP) and the loss percentage. Then, we will calculate the gain or loss percentage when the article is sold for a different price.

### Step 1: Determine the Cost Price (CP)
Given:
- Selling Price (SP) = 69
- Loss Percentage = 8%

The formula for loss percentage is:
\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{Cost Price}} \times 100 \]
Since there is a loss of 8%, we can express the loss in terms of CP:
\[ \text{Loss} = \frac{8}{100} \times \text{CP} = \frac{2}{25} \times \text{CP} \]
This means that the Selling Price can be expressed as:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Substituting the loss into the equation:
\[ 69 = \text{CP} - \frac{2}{25} \times \text{CP} \]
This simplifies to:
\[ 69 = \text{CP} \left(1 - \frac{2}{25}\right) = \text{CP} \left(\frac{25 - 2}{25}\right) = \text{CP} \left(\frac{23}{25}\right) \]
Now, we can solve for CP:
\[ \text{CP} = 69 \times \frac{25}{23} \]
Calculating this gives:
\[ \text{CP} = 75 \]

### Step 2: Calculate Gain or Loss Percentage when SP = 78
Now, we need to find the gain or loss percentage when the article is sold for 78.

Given:
- New Selling Price (SP) = 78
- Cost Price (CP) = 75

The gain can be calculated as:
\[ \text{Gain} = \text{SP} - \text{CP} = 78 - 75 = 3 \]

Now, we can calculate the gain percentage using the formula:
\[ \text{Gain Percentage} = \frac{\text{Gain}}{\text{CP}} \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \frac{3}{75} \times 100 \]
Calculating this gives:
\[ \text{Gain Percentage} = 4\% \]

### Final Answer
The gain percentage when the article is sold for 78 is **4%**.