In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the prifit

Options

A. 0.7
B. 0.8
C. 0.9
D. None of above

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Define the Cost Price (CP) and Selling Price (SP)
Let’s assume the Cost Price (CP) is 100 units.

### Step 2: Calculate the Profit
Given that the profit is 320% of the cost price:
\[ \text{Profit} = 320\% \text{ of CP} = 320\% \times 100 = 320 \text{ units} \]

### Step 3: Calculate the Selling Price (SP)
The Selling Price (SP) is calculated as:
\[ \text{SP} = \text{CP} + \text{Profit} = 100 + 320 = 420 \text{ units} \]

### Step 4: Increase the Cost Price by 25%
Now, if the cost increases by 25%, the new Cost Price (CP') will be:
\[ \text{CP'} = \text{CP} + 25\% \text{ of CP} = 100 + 25 = 125 \text{ units} \]

### Step 5: Calculate the New Profit
Since the Selling Price remains constant at 420 units, the new Profit (Profit') will be:
\[ \text{Profit'} = \text{SP} - \text{CP'} = 420 - 125 = 295 \text{ units} \]

### Step 6: Calculate the Profit as a Percentage of the Selling Price
To find out what percentage of the Selling Price the new profit is, we use the formula:
\[ \text{Percentage of Profit} = \left( \frac{\text{Profit'}}{\text{SP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage of Profit} = \left( \frac{295}{420} \right) \times 100 \]

### Step 7: Simplify the Calculation
Calculating the above expression:
\[ \text{Percentage of Profit} = \left( \frac{2950}{420} \right) \approx 70.24\% \]
Thus, approximately, the profit is about 70%.

### Conclusion
The approximate percentage of the selling price that is the profit is **0.7** or **70%**.

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