If the cost price of 10 pens is equal to the selling price of 8 pens, find the gain or loss per cent.

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas for profit and loss.

### Step 1: Understand the relationship between Cost Price (CP) and Selling Price (SP)
We are given that the cost price of 10 pens is equal to the selling price of 8 pens. This can be expressed mathematically as:
\[ \text{Cost Price of 10 pens} = \text{Selling Price of 8 pens} \]

### Step 2: Define the Cost Price and Selling Price of one pen
Let the cost price of one pen be \( CP \) and the selling price of one pen be \( SP \).

From the information given:
\[ 10 \times CP = 8 \times SP \]

### Step 3: Rearranging the equation
We can rearrange the equation to find the relationship between SP and CP:
\[ SP = \frac{10}{8} \times CP \]
\[ SP = \frac{5}{4} \times CP \]

### Step 4: Calculate the profit
Now, we can find the profit made on selling one pen:
\[ \text{Profit} = SP - CP \]
Substituting the value of SP from the previous step:
\[ \text{Profit} = \left(\frac{5}{4} \times CP\right) - CP \]
\[ \text{Profit} = \left(\frac{5}{4} - 1\right) \times CP \]
\[ \text{Profit} = \left(\frac{5}{4} - \frac{4}{4}\right) \times CP \]
\[ \text{Profit} = \frac{1}{4} \times CP \]

### Step 5: Calculate the profit percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
Substituting the profit we calculated:
\[ \text{Profit Percentage} = \left(\frac{\frac{1}{4} \times CP}{CP}\right) \times 100 \]
\[ \text{Profit Percentage} = \left(\frac{1}{4}\right) \times 100 \]
\[ \text{Profit Percentage} = 25\% \]

### Conclusion
The gain percentage is 25%.

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