If the selling price is tripled and cost price doubled the profit would become 65%. What is the present profit (in %)?

Options

A. 20
B. 15
C. 25
D. 10

Answer

To solve the problem step by step, let's denote the cost price as \( CP = X \) and the selling price as \( SP = Y \).

### Step 1: Define the Profit
The profit can be defined as:
\[ \text{Profit} = SP - CP = Y - X \]

### Step 2: Analyze the Changes
According to the problem, if the cost price is doubled, it becomes \( 2X \), and if the selling price is tripled, it becomes \( 3Y \). The new profit in this case will be:
\[ \text{New Profit} = 3Y - 2X \]

### Step 3: Set Up the Profit Equation
The problem states that this new profit corresponds to a profit of 65%. Therefore, we can express this as:
\[ 3Y - 2X = 0.65 \times (2X) \]
This simplifies to:
\[ 3Y - 2X = 1.3X \]

### Step 4: Rearrange the Equation
Rearranging the equation gives us:
\[ 3Y = 1.3X + 2X \]
\[ 3Y = 3.3X \]

### Step 5: Solve for \( Y \) in terms of \( X \)
Dividing both sides by 3:
\[ Y = 1.1X \]

### Step 6: Calculate the Present Profit
Now, we can calculate the present profit using the original profit formula:
\[ \text{Present Profit} = Y - X = 1.1X - X = 0.1X \]
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{0.1X}{X}\right) \times 100 = 10\% \]

### Final Answer
Thus, the present profit percentage is:
\[ \text{Present Profit Percentage} = 10\% \]