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The question asks about the profit on a book sold at a 20% discount, given that the marked price is $ x $ and 30% of this price is profit. Let's break this down step by step:

1. **Marked Price:** The original price of the book is $ x $.
   
2. **Profit at Full Price:** The problem states that 30% of the marked price is profit. So, the profit at full price is:
   \[
   \text{Profit at full price} = 0.30x
   \]

3. **Selling Price with Discount:** If the book is sold at a 20% discount, the selling price becomes:
   \[
   \text{Selling price} = x - 0.20x = 0.80x
   \]
   
4. **Profit on the Discounted Price:** The profit is the difference between the selling price and the cost price (assuming the cost price is the remaining amount after taking the original profit into account):
   \[
   \text{Cost price} = x - 0.30x = 0.70x
   \]
   So, the profit when sold at a discount is:
   \[
   \text{Profit on discounted price} = 0.80x - 0.70x = 0.10x
   \]

Thus, the profit when the book is sold at a 20% discount is $ 0.10x $, which corresponds to **option C**.

Let me know if you need further explanation or have more questions! Here are some related questions to practice:

1. What is the new profit if the book is sold at a 30% discount?
2. How does the profit change if the profit percentage is increased to 40%?
3. If the cost price is known, how would you calculate the profit directly?
4. What would the profit be if no discount is applied but the profit percentage increases to 50%?
5. How do you calculate the selling price if you want a specific profit?

**Tip:** Always differentiate between the marked price, selling price, and cost price to avoid confusion in percentage problems.

The marked price of a book is $x. 30% of this price is profit. If the book is sold at a discount of 20%, what will the profit then be?

Learn how to calculate profit when a book is sold at a 20% discount, given that 30% of the marked price is profit. This problem covers percentage calculations, profit, and loss concepts suitable for Grades 7-9.

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