On an article the profit is 230% of the cost price. If the cost price increases by 50% but the selling price remains constant, then what is the new profit per cent?

Options

A. 54.54
B. 80
C. 120
D. 150

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given information
We know that the profit is 230% of the cost price (CP).

### Step 2: Define the cost price
Let’s assume the cost price (CP) of the article is ₹100.

### Step 3: Calculate the profit
Since the profit is 230% of the cost price:
\[ \text{Profit} = 230\% \text{ of } 100 = \frac{230}{100} \times 100 = ₹230 \]

### Step 4: Calculate the selling price (SP)
The selling price (SP) can be calculated using the formula:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
Substituting the values:
\[ \text{SP} = 100 + 230 = ₹330 \]

### Step 5: Update the cost price
Now, the cost price increases by 50%. Therefore, the new cost price (CP') is:
\[ \text{New CP} = 100 + 50\% \text{ of } 100 = 100 + 50 = ₹150 \]

### Step 6: Selling price remains constant
The selling price remains the same at ₹330.

### Step 7: Calculate the new profit
Now, we can calculate the new profit (Profit'):
\[ \text{Profit'} = \text{Selling Price} - \text{New Cost Price} = 330 - 150 = ₹180 \]

### Step 8: Calculate the new profit percentage
The new profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit'}}{\text{New CP}} \times 100\right) \]
Substituting the values:
\[ \text{Profit Percentage} = \left(\frac{180}{150} \times 100\right) \]
\[ = \left(1.2 \times 100\right) = 120\% \]

### Final Answer
The new profit percentage is **120%**.

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