If the cost price of 15 books is equal to the selling price of 20 books, the loss percent is

Options

A. 16
B. 20
C. 24
D. 25

Answer

To solve the problem, we need to find the loss percentage when the cost price of 15 books is equal to the selling price of 20 books. Here’s a step-by-step solution:

### Step 1: Establish the relationship between Cost Price (CP) and Selling Price (SP)
According to the problem, the cost price of 15 books is equal to the selling price of 20 books. We can express this relationship mathematically:

\[ CP \text{ of } 15 \text{ books} = SP \text{ of } 20 \text{ books} \]

### Step 2: Let’s assume the cost price of one book
Let the cost price of one book be \( k \). Therefore, the cost price of 15 books will be:

\[ CP = 15k \]

### Step 3: Let’s express the selling price of one book
Let the selling price of one book be \( m \). Therefore, the selling price of 20 books will be:

\[ SP = 20m \]

### Step 4: Set up the equation based on the relationship
From the information given, we have:

\[ 15k = 20m \]

### Step 5: Solve for the ratio of CP to SP
To find the ratio of CP to SP, we can rearrange the equation:

\[ \frac{CP}{SP} = \frac{20m}{15k} = \frac{20}{15} = \frac{4}{3} \]

### Step 6: Express CP and SP in terms of a common variable
Let’s express CP and SP in terms of a common variable \( x \):

\[ CP = 4x \quad \text{and} \quad SP = 3x \]

### Step 7: Calculate the loss
Loss can be calculated as:

\[ \text{Loss} = CP - SP = 4x - 3x = x \]

### Step 8: Calculate the loss percentage
Loss percentage is calculated using the formula:

\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]

Substituting the values we have:

\[ \text{Loss Percentage} = \left(\frac{x}{4x}\right) \times 100 = \frac{1}{4} \times 100 = 25\% \]

### Final Answer
The loss percentage is **25%**.

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