The cost price of 12 tables is equal to the selling price of 16 tables. The loss percent is

Options

A. `15%`
B. `20%`
C. `25%`
D. `30%`

Answer

To solve the problem, we need to find the loss percentage when the cost price of 12 tables is equal to the selling price of 16 tables.

### Step 1: Define Variables
Let the cost price of one table be \( CP \) and the selling price of one table be \( SP \).

### Step 2: Write the Given Information
According to the problem:
- The cost price of 12 tables is \( 12 \times CP \).
- The selling price of 16 tables is \( 16 \times SP \).

From the problem statement, we have:
\[ 12 \times CP = 16 \times SP \]

### Step 3: Rearrange the Equation
We can rearrange this equation to express \( SP \) in terms of \( CP \):
\[ SP = \frac{12 \times CP}{16} \]
\[ SP = \frac{3}{4} \times CP \]

### Step 4: Calculate the Loss
The loss incurred when selling the tables can be calculated as:
\[ \text{Loss} = CP - SP \]
Substituting the value of \( SP \):
\[ \text{Loss} = CP - \frac{3}{4} \times CP \]
\[ \text{Loss} = CP \left(1 - \frac{3}{4}\right) \]
\[ \text{Loss} = CP \times \frac{1}{4} \]

### Step 5: Calculate the Loss Percentage
The loss percentage is given by the formula:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100\% \]
Substituting the value of Loss:
\[ \text{Loss Percentage} = \left(\frac{CP \times \frac{1}{4}}{CP}\right) \times 100\% \]
\[ \text{Loss Percentage} = \frac{1}{4} \times 100\% \]
\[ \text{Loss Percentage} = 25\% \]

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

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