The cost price of an item is two-third of its selling price.What is the gain or loss percent on that item?

Options

A. 45
B. 50
C. 35
D. 54

Answer

To solve the question step by step, we will follow these instructions:

### Step 1: Understand the relationship between Cost Price (CP) and Selling Price (SP)
We are given that the cost price of an item is two-thirds of its selling price. This can be expressed mathematically as:
\[ CP = \frac{2}{3} \times SP \]

### Step 2: Assign values to CP and SP
To simplify calculations, we can assign a value to SP. Let's assume:
\[ SP = 3x \]
Then, substituting this into the equation for CP:
\[ CP = \frac{2}{3} \times (3x) = 2x \]

### Step 3: Calculate Profit
Profit (P) is calculated as the difference between Selling Price and Cost Price:
\[ P = SP - CP \]
Substituting the values we assigned:
\[ P = 3x - 2x = x \]

### Step 4: Calculate Gain Percentage
Gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{P}{CP} \right) \times 100 \]
Substituting the values of P and CP:
\[ \text{Gain Percentage} = \left( \frac{x}{2x} \right) \times 100 = \left( \frac{1}{2} \right) \times 100 = 50\% \]

### Conclusion
The gain percentage on the item is **50%**.

---