If the selling price is tripled, the profit becomes 5 times. Whatis the profit percent?

Options

A. 1
B. 2
C. 0.5
D. 1.5

Answer

To solve the problem step by step, we will denote the Cost Price (CP) and Selling Price (SP) and use the information given in the question.

### Step 1: Define the variables
Let:
- Cost Price (CP) = x
- Selling Price (SP) = y

### Step 2: Understand the relationship between SP and profit
The profit is given by the formula:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
So, we can express profit as:
\[ \text{Profit} = y - x \]

### Step 3: Analyze the effect of tripling the Selling Price
According to the question, if the Selling Price is tripled, the new Selling Price becomes:
\[ \text{New SP} = 3y \]

### Step 4: Set up the equation for the new profit
The new profit when the Selling Price is tripled is:
\[ \text{New Profit} = \text{New SP} - \text{CP} = 3y - x \]
According to the problem, this new profit is five times the original profit:
\[ 3y - x = 5(y - x) \]

### Step 5: Expand and rearrange the equation
Expanding the right side gives:
\[ 3y - x = 5y - 5x \]
Now, rearranging the equation:
\[ 3y - x + 5x = 5y \]
\[ 3y + 4x = 5y \]
Subtracting \(3y\) from both sides:
\[ 4x = 5y - 3y \]
\[ 4x = 2y \]

### Step 6: Solve for the relationship between CP and SP
Dividing both sides by 2 gives:
\[ 2x = y \]
This means:
\[ y = 2x \]
So, the Selling Price is twice the Cost Price.

### Step 7: Calculate the profit
Now, we can calculate the profit:
\[ \text{Profit} = y - x = 2x - x = x \]

### Step 8: Calculate the profit percentage
The profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{x}{x} \right) \times 100 = 100\% \]

### Final Answer
The profit percentage is **100%**.