If a commission of 10% is given on the marked price of a book, the publiser gains 20%. If the commission is increased to 15%, the gain of publisher is:

Options

A. 0.1333
B. 0.15
C. 0.18
D. data insufficient

Answer

To solve the problem step by step, we will first define the variables and then calculate the required values based on the information given in the question.

### Step 1: Define the Cost Price (CP) and Marked Price (MP)
Let's assume the Cost Price (CP) of the book is 100 units (this makes calculations easier).

### Step 2: Calculate the Selling Price (SP) with 10% Commission
Given that the publisher gains 20%, we can calculate the Selling Price (SP) as follows:
- Gain = 20% of CP = 20% of 100 = 20
- Therefore, SP = CP + Gain = 100 + 20 = 120 units.

### Step 3: Relate Selling Price to Marked Price with 10% Commission
When a 10% commission is given on the Marked Price (MP), the Selling Price can also be expressed as:
- SP = MP - 10% of MP
- SP = MP - (10/100) * MP = MP - 0.1 * MP = 0.9 * MP.

### Step 4: Set up the Equation
Now, we can set up the equation based on the Selling Price:
- 120 = 0.9 * MP.
- To find MP, we rearrange the equation: MP = 120 / 0.9 = 133.33 units.

### Step 5: Calculate Selling Price with 15% Commission
Now, we need to find the Selling Price when the commission is increased to 15%:
- SP = MP - 15% of MP
- SP = MP - (15/100) * MP = MP - 0.15 * MP = 0.85 * MP.

### Step 6: Substitute the Marked Price
Substituting the value of MP we found earlier:
- SP = 0.85 * 133.33 = 113.33 units.

### Step 7: Calculate the Gain with 15% Commission
Now, we can find the gain for the publisher when the commission is 15%:
- Gain = SP - CP = 113.33 - 100 = 13.33 units.

### Step 8: Calculate the Gain Percentage
To find the gain percentage:
- Gain Percentage = (Gain / CP) * 100 = (13.33 / 100) * 100 = 13.33%.

### Step 9: Convert Gain Percentage to Decimal
To express the gain in decimal form:
- Gain in decimal = 13.33 / 100 = 0.1333.

### Final Answer
Thus, the gain of the publisher when the commission is increased to 15% is **0.1333** or **13.33%**.

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