The selling price of a chair is `33/20` times its cost price. What is the gain or loss percentage in the transaction ?

Options

A. Loss, `35%`
B. Loss, `65%`
C. Gain, `35%`
D. Gain, `65%`

Answer

To find the gain or loss percentage in the transaction, we can follow these steps:

### Step 1: Define the Cost Price (CP)
Let the cost price of the chair be denoted as \( CP \).

### Step 2: Calculate the Selling Price (SP)
According to the problem, the selling price (SP) is given as \( \frac{33}{20} \) times the cost price. Therefore, we can express the selling price as:
\[ SP = \frac{33}{20} \times CP \]

### Step 3: Determine the Gain
The gain can be calculated using the formula:
\[ \text{Gain} = SP - CP \]
Substituting the expression for SP, we have:
\[ \text{Gain} = \left(\frac{33}{20} \times CP\right) - CP \]
To combine the terms, we can express \( CP \) as \( \frac{20}{20} \times CP \):
\[ \text{Gain} = \left(\frac{33}{20} \times CP\right) - \left(\frac{20}{20} \times CP\right) = \frac{33 - 20}{20} \times CP = \frac{13}{20} \times CP \]

### Step 4: Calculate the Gain Percentage
The gain percentage is given by the formula:
\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{CP}\right) \times 100 \]
Substituting the gain we found:
\[ \text{Gain Percentage} = \left(\frac{\frac{13}{20} \times CP}{CP}\right) \times 100 = \left(\frac{13}{20}\right) \times 100 \]
Calculating this gives:
\[ \text{Gain Percentage} = \frac{1300}{20} = 65\% \]

### Final Answer
The gain percentage in the transaction is **65%**.

---