A bookseller buys books at a discount of 25% on the marked price. How much per cent discount should be offer so as to gain 20% on the sale?

Options

A. `25% `
B. `20% `
C. `30% `
D. `10% `

Answer

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

### Step 1: Understand the Given Information
- The bookseller buys books at a **25% discount** on the marked price.
- The bookseller wants to gain a **20% profit** on the sale.

### Step 2: Define the Marked Price (MP)
Let's assume the **Marked Price (MP)** of the book is **100** (this is a convenient assumption to simplify calculations).

### Step 3: Calculate the Cost Price (CP)
Since the bookseller gets a **25% discount** on the marked price:
- Discount = 25% of 100 = 25
- Therefore, the Cost Price (CP) = Marked Price - Discount = 100 - 25 = **75**.

### Step 4: Calculate the Selling Price (SP) for a 20% Profit
To gain a **20% profit** on the Cost Price:
- Profit = 20% of CP = 20% of 75 = 15.
- Therefore, the Selling Price (SP) = Cost Price + Profit = 75 + 15 = **90**.

### Step 5: Calculate the Required Selling Price in Terms of Discount
Now, we need to find out what percentage discount should be offered on the marked price to sell the book for **90**.
- Selling Price (SP) = Marked Price (MP) - Discount
- Let the discount be **D**. Then:
\[ 90 = 100 - D \]
- Rearranging gives:
\[ D = 100 - 90 = 10 \]

### Step 6: Calculate the Percentage Discount
The percentage discount is calculated as:
\[ \text{Percentage Discount} = \left(\frac{D}{MP}\right) \times 100 = \left(\frac{10}{100}\right) \times 100 = 10\% \]

### Final Answer
The bookseller should offer a **10% discount** to gain a 20% profit on the sale.

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