https://file.aiquickdraw.com/mathbot/file/1727022497191r9wcfazf.jpg

To solve this problem, let's break it down step by step:

### Given:
- The **marked price** of the book is **$240**.
- The book is sold at a **20% discount** on the marked price.
- The **profit** is 20% of the **cost price**.

We need to find the **cost price** of the book.

### Step 1: Calculate the Selling Price
The discount is 20%, so the selling price can be found as:
\[
\text{Selling Price} = \text{Marked Price} - \left( \text{20% of Marked Price} \right)
\]
\[
\text{Selling Price} = 240 - (20\% \times 240) = 240 - 48 = 192
\]

### Step 2: Profit Calculation
The profit is given as 20% of the cost price. Let the cost price be denoted as $ C $. So, the profit is:
\[
\text{Profit} = 20\% \times C = 0.2C
\]

### Step 3: Relationship Between Selling Price and Cost Price
The selling price is equal to the cost price plus the profit:
\[
\text{Selling Price} = C + 0.2C = 1.2C
\]
From Step 1, we know the selling price is **$192**:
\[
192 = 1.2C
\]

### Step 4: Solve for the Cost Price
\[
C = \frac{192}{1.2} = 160
\]

### Final Answer:
The cost price of the book is **$160**, which corresponds to option **A**.

---

Would you like more details or have any questions?

Here are 5 related questions you could explore:
1. How would the cost price change if the discount were 30% instead of 20%?
2. What would be the profit percentage if the selling price remained the same but the cost price was $180?
3. How do we calculate the marked price if we know the cost price and the desired profit percentage?
4. What if the profit was 25% of the cost price? How would that affect the cost price?
5. Can we calculate the cost price if only the profit and selling price are known?

**Tip:** Always verify whether the profit percentage is based on the cost price or the selling price; this can change the calculations.

The marked price of a book is $240. If the book is sold at a discount of 20%, the profit will be 20% of the cost price. What is the cost price of the book?

Solve the problem of determining the cost price of a book when given the marked price of $240, a discount of 20%, and a profit of 20%. This problem involves basic profit and discount calculations suitable for Grades 8-10.

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