On a certain item profit is 150%. If the cost price increases by 25% what will be the new profit margin (in %)?

Options

A. 25
B. 50
C. 100
D. 75

Answer

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

### Step 1: Determine the Initial Cost Price (CP) and Selling Price (SP)
Let the initial Cost Price (CP) be \( 100 \) (this is a convenient choice for calculation).

Given that the profit is \( 150\% \), we can calculate the Selling Price (SP) using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} \]
The profit can be calculated as:
\[ \text{Profit} = \frac{150}{100} \times \text{CP} = \frac{150}{100} \times 100 = 150 \]
Now, substituting the values:
\[ \text{SP} = 100 + 150 = 250 \]

### Step 2: Calculate the New Cost Price after Increase
The cost price increases by \( 25\% \). Therefore, the new Cost Price (CP') can be calculated as:
\[ \text{CP'} = \text{CP} + \left( \frac{25}{100} \times \text{CP} \right) \]
Calculating this gives:
\[ \text{CP'} = 100 + \left( \frac{25}{100} \times 100 \right) = 100 + 25 = 125 \]

### Step 3: Calculate the New Profit
Now, we need to calculate the new profit using the new Cost Price (CP'):
\[ \text{New Profit} = \text{SP} - \text{CP'} = 250 - 125 = 125 \]

### Step 4: Calculate the New Profit Margin
The new profit margin can be calculated using the formula:
\[ \text{New Profit Margin (\%)} = \left( \frac{\text{New Profit}}{\text{CP'}} \right) \times 100 \]
Substituting the values:
\[ \text{New Profit Margin (\%)} = \left( \frac{125}{125} \right) \times 100 = 100\% \]

### Final Answer
The new profit margin is \( 100\% \).

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