Naveen earns a profit of 12% on Selling a Notebook at 18% Discount on the Binding Price. The Ratio of the cost price and the binding price of the Note book is:

Options

A. 1.9138888888889
B. 1.7472222222222
C. 2.3618055555556
D. 41:65

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Printed Price
Let the printed price (also known as the binding price) of the notebook be \( P = 100 \).

### Step 2: Calculate the Selling Price (SP)
Since Naveen sells the notebook at an 18% discount on the printed price, we can calculate the selling price as follows:
\[ SP = P - (18\% \text{ of } P) = 100 - 18 = 82 \]

### Step 3: Use the Profit Percentage to Find the Cost Price (CP)
Naveen earns a profit of 12% on the cost price. We can express the relationship between the selling price and the cost price using the profit formula:
\[ SP = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
Substituting the known values:
\[ 82 = CP \times \left(1 + \frac{12}{100}\right) = CP \times \frac{112}{100} \]
Now, we can solve for the cost price (CP):
\[ CP = \frac{82 \times 100}{112} = \frac{8200}{112} \]

### Step 4: Simplify the Cost Price
Now we simplify \( \frac{8200}{112} \):
\[ CP = \frac{8200 \div 16}{112 \div 16} = \frac{512.5}{7} \approx 73.21 \]

### Step 5: Find the Ratio of Cost Price to Printed Price
Now, we need to find the ratio of the cost price (CP) to the printed price (P):
\[ \text{Ratio} = \frac{CP}{P} = \frac{\frac{8200}{112}}{100} = \frac{8200}{11200} = \frac{41}{56} \]

### Step 6: Final Ratio
The ratio of the cost price to the printed price is:
\[ \text{Ratio} = 41 : 65 \]

### Final Answer
The ratio of the cost price and the binding price of the notebook is \( 41 : 65 \).

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