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9. A shopkeeper marks his goods at [tex]$25 \%$[/tex] above the cost price and gives a [tex]$15 \%$[/tex] discount. Find his gain or loss percentage.

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To solve this problem, we will follow these steps:

1. Identify the cost price (CP): Let's assume the cost price is 100 units, for simplicity.

2. Calculate the marked price (MP): The shopkeeper marks his goods at 25% above the cost price.
- Marked Price (MP) = Cost Price (CP) + 25% of Cost Price
- MP = CP + (25% of CP)
- MP = 100 + 25% of 100
- MP = 100 + 25
- MP = 125 units

3. Calculate the selling price (SP) after the discount: The shopkeeper offers a 15% discount on the marked price.
- Discount = 15% of MP
- Discount = 15% of 125
- Discount = 0.15 × 125
- Discount = 18.75 units
- Selling Price (SP) = Marked Price (MP) - Discount
- SP = 125 - 18.75
- SP = 106.25 units

4. Determine whether there is a gain or loss and calculate the percentage: Compare the selling price with the cost price to find the gain or loss percentage.
- Profit or Loss = Selling Price (SP) - Cost Price (CP)
- Profit or Loss = 106.25 - 100
- Profit or Loss = 6.25 (Since it's positive, it is a gain)
- Gain Percentage = (Gain / Cost Price) × 100
- Gain Percentage = (6.25 / 100) × 100
- Gain Percentage = 6.25%

Thus, the shopkeeper's gain percentage is 6.25%.
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