A discount of 16% on the marked price of a book enables a man to buy a pen that costs Rs. 80. How much did he pay for the book ?

Options

A. Rs. 500
B. Rs. 480
C. Rs. 420
D. Rs. 340

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the relationship between the discount and the cost of the pen.
The problem states that a discount of 16% on the marked price of a book allows a man to buy a pen that costs Rs. 80. This means that the amount saved from the discount on the book is equal to the price of the pen.

### Step 2: Define the marked price of the book.
Let the marked price of the book be denoted as \( X \).

### Step 3: Calculate the discount amount.
The discount on the book is 16% of the marked price \( X \). This can be expressed mathematically as:
\[ \text{Discount} = 0.16 \times X \]

### Step 4: Set up the equation.
According to the problem, the discount amount is equal to the cost of the pen, which is Rs. 80. Therefore, we can set up the equation:
\[ 0.16 \times X = 80 \]

### Step 5: Solve for \( X \).
To find \( X \), we can rearrange the equation:
\[ X = \frac{80}{0.16} \]

Calculating this gives:
\[ X = 500 \]

### Step 6: Calculate the selling price of the book.
The selling price (the price he actually pays for the book) can be calculated by subtracting the discount from the marked price:
\[ \text{Selling Price} = X - \text{Discount} \]
The discount can be calculated as:
\[ \text{Discount} = 0.16 \times 500 = 80 \]
So, the selling price is:
\[ \text{Selling Price} = 500 - 80 = 420 \]

### Conclusion
The man paid Rs. 420 for the book.

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