Let's solve this problem step by step:

Step 1: Understanding the Problem

• Markup: The shopkeeper marks up the product by 60%. This means the selling price (without discount) becomes 160% of the cost price (CP).
• Discount: A 30% discount is given on this marked price.

Step 2: Expressing Marked Price and Discount

• Let the Cost Price (CP) be $x$.

• After a 60% markup, the Marked Price (MP) becomes: $MP = x \times (1 + 0.60) = 1.6x$

• Now, a 30% discount is given on this marked price, so the Selling Price (SP) becomes: $SP = 1.6x \times (1 - 0.30) = 1.6x \times 0.70 = 1.12x$

Step 3: Calculating Profit Percentage

• Profit/Loss is calculated using the formula: $\text{Profit Percentage} = \left(\frac{\text{SP} - \text{CP}}{\text{CP}}\right) \times 100$

• Substituting the values, we get: $\text{Profit Percentage} = \left(\frac{1.12x - x}{x}\right) \times 100 = \left(\frac{0.12x}{x}\right) \times 100 = 12\%$

Final Answer

The shopkeeper gains a profit of 12%.

Would you like more details or have any other questions? Here are some related questions for further practice:

1. What would be the loss percentage if the shopkeeper had given a 50% discount instead?
2. If the cost price is $100, what would be the marked price and selling price?
3. How much profit would the shopkeeper make if no discount was given?
4. What is the new selling price if the markup is 80% and a discount of 20% is given?
5. If the profit percentage needs to be 20%, what should the discount be for a 60% markup?

Tip: When dealing with markups and discounts, always work through the percentages step by step to avoid confusion and ensure accuracy.