On a certain item profit is 120%. If the cost price increases by 10% then what will be the new profit margin (in% ) if selling price remains the same?

Options

A. 0.5
B. 0.6
C. 100
D. 90

Answer

To solve the problem, we need to follow these steps:

### Step 1: Understand the given information
We know that the profit percentage on an item is 120%. This means that the profit earned on the cost price (CP) is 120% of CP.

### Step 2: Define the cost price (CP) and selling price (SP)
Let the cost price (CP) be \( x \).
Since the profit is 120%, the selling price (SP) can be calculated as:
\[ SP = CP + Profit = CP + (120\% \text{ of } CP) = x + 1.2x = 2.2x \]

### Step 3: Calculate the new cost price after a 10% increase
If the cost price increases by 10%, the new cost price (CP') will be:
\[ CP' = CP + (10\% \text{ of } CP) = x + 0.1x = 1.1x \]

### Step 4: Determine the new profit
Since the selling price remains the same, we will use the original selling price (SP = 2.2x) to find the new profit:
\[ \text{New Profit} = SP - CP' = 2.2x - 1.1x = 1.1x \]

### Step 5: Calculate the new profit margin percentage
The profit margin percentage is calculated based on the new cost price (CP'):
\[ \text{New Profit Margin} = \left( \frac{\text{New Profit}}{CP'} \right) \times 100 = \left( \frac{1.1x}{1.1x} \right) \times 100 = 100\% \]

### Final Answer
The new profit margin, after a 10% increase in cost price while keeping the selling price constant, is **100%**.

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