A shopkeeper earns a profit of 15% on selling a book at 15% 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. `23:17`
D. `17:23`

Answer

To solve the problem step by step, we will follow the information provided in the question and apply the relevant formulas.

### Step 1: Understand the given information
- Profit percentage = 15%
- Discount percentage = 15%

### Step 2: Use the formula for the ratio of Mark Price (MP) to Cost Price (CP)
The formula to find the ratio of Mark Price to Cost Price when profit and discount percentages are given is:
\[ \frac{MP}{CP} = \frac{100 + \text{Profit Percentage}}{100 - \text{Discount Percentage}} \]

### Step 3: Substitute the values into the formula
Substituting the given percentages into the formula:
\[ \frac{MP}{CP} = \frac{100 + 15}{100 - 15} = \frac{115}{85} \]

### Step 4: Simplify the fraction
Now, we simplify the fraction:
\[ \frac{115}{85} = \frac{23}{17} \]

### Step 5: Find the ratio of Cost Price to Mark Price
We need to find the ratio of Cost Price (CP) to Mark Price (MP), which is the reciprocal of the ratio we just found:
\[ \frac{CP}{MP} = \frac{17}{23} \]

### Step 6: Write the final answer
Thus, the ratio of the Cost Price to the Mark Price is:
\[ \text{Cost Price : Mark Price} = 17 : 23 \]

### Conclusion
The correct answer is Option 4: 17 : 23.

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