A shokeeper earns a profit of `15%` after selling a book at `20%` discount on the printed price .the ratio of the cost price and the printed price of the book is

Options

A. `20 : 23`
B. `23 : 20`
C. `16 : 23`
D. `23 : 16`

Answer

To solve the problem step by step, let's denote:

- Cost Price (C) of the book
- Printed Price (P) of the book

### Step 1: Determine the Selling Price based on Profit
The shopkeeper earns a profit of 15%. Therefore, the Selling Price (SP) can be calculated as follows:

\[ SP = C + \text{Profit} = C + 0.15C = 1.15C \]

### Step 2: Determine the Selling Price based on Discount
The shopkeeper sells the book at a 20% discount on the Printed Price (P). The discount amount can be calculated as:

\[ \text{Discount} = 20\% \text{ of } P = 0.20P \]

Thus, the Selling Price (SP) based on the Printed Price is:

\[ SP = P - \text{Discount} = P - 0.20P = 0.80P \]

### Step 3: Set the Two Expressions for Selling Price Equal
Since both expressions represent the Selling Price, we can set them equal to each other:

\[ 1.15C = 0.80P \]

### Step 4: Rearranging to Find the Ratio of C to P
To find the ratio of Cost Price (C) to Printed Price (P), we rearrange the equation:

\[ \frac{C}{P} = \frac{0.80}{1.15} \]

### Step 5: Simplifying the Ratio
Now, we simplify the fraction:

\[ \frac{C}{P} = \frac{0.80 \times 100}{1.15 \times 100} = \frac{80}{115} \]

Next, we simplify \( \frac{80}{115} \):

- Both 80 and 115 can be divided by 5:
\[ \frac{80 \div 5}{115 \div 5} = \frac{16}{23} \]

### Conclusion
Thus, the ratio of the Cost Price (C) to the Printed Price (P) is:

\[ C : P = 16 : 23 \]