The marked price of a pen and pencil are in the ratio 1:2. The shopkeeper gives 40% discount on the pen. If the total discount on the set of the pen and pencil is 30%, the discount offered on the pencil is.

Options

A. 0.15
B. 0.2
C. 0.25
D. 0.3

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Define the Marked Prices
Let the marked price of the pen be \( x \). Then, the marked price of the pencil will be \( 2x \) since the ratio of the marked prices is 1:2.

### Step 2: Calculate Total Marked Price
The total marked price of both the pen and pencil is:
\[ \text{Total Marked Price} = x + 2x = 3x \]

### Step 3: Calculate the Discount on the Pen
The shopkeeper gives a 40% discount on the pen. Therefore, the selling price of the pen after discount is:
\[ \text{Selling Price of Pen} = x - 0.40x = 0.60x \]

### Step 4: Calculate the Total Discount on the Set
The total discount on the set of pen and pencil is 30%. Thus, the selling price of the entire set after a 30% discount is:
\[ \text{Selling Price of Set} = \text{Total Marked Price} - 30\% \text{ of Total Marked Price} = 3x - 0.30(3x) = 3x - 0.90x = 2.10x \]

### Step 5: Calculate the Selling Price of the Pencil
Let the selling price of the pencil be \( SP_p \). The total selling price of the set (pen + pencil) is:
\[ \text{Selling Price of Set} = \text{Selling Price of Pen} + \text{Selling Price of Pencil} \]
Substituting the known values:
\[ 2.10x = 0.60x + SP_p \]
Now, solve for \( SP_p \):
\[ SP_p = 2.10x - 0.60x = 1.50x \]

### Step 6: Calculate the Discount on the Pencil
The marked price of the pencil is \( 2x \). The selling price of the pencil is \( 1.50x \). The discount on the pencil can be calculated as follows:
\[ \text{Discount on Pencil} = \text{Marked Price of Pencil} - \text{Selling Price of Pencil} = 2x - 1.50x = 0.50x \]

### Step 7: Calculate the Percentage Discount on the Pencil
The percentage discount on the pencil is given by:
\[ \text{Percentage Discount} = \left( \frac{\text{Discount on Pencil}}{\text{Marked Price of Pencil}} \right) \times 100 = \left( \frac{0.50x}{2x} \right) \times 100 = \frac{0.50}{2} \times 100 = 25\% \]

### Final Answer
The discount offered on the pencil is **25%**.

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