On an article the profit is 210% of the cost price. If the cost price increase by 40% but the selling price remains constant, then approximately what percentage of selling price will be the profit?

Options

A. 55
B. 62
C. 74
D. 85

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Understand the Initial Conditions
The profit on the article is given as 210% of the cost price (CP).
Let the initial cost price (CP1) be \( CP1 = 100 \) (for simplicity).

### Step 2: Calculate the Selling Price (SP)
The profit is 210% of the cost price, so:
\[ \text{Profit} = 210\% \times CP1 = 210\% \times 100 = 210 \]
Now, the selling price (SP) can be calculated as:
\[ SP = CP1 + \text{Profit} = 100 + 210 = 310 \]

### Step 3: Calculate the New Cost Price After Increase
The cost price increases by 40%. Therefore, the new cost price (CP2) is:
\[ CP2 = CP1 + 40\% \times CP1 = 100 + 40\% \times 100 = 100 + 40 = 140 \]

### Step 4: Calculate the New Profit
Since the selling price remains constant, we can calculate the new profit:
\[ \text{New Profit} = SP - CP2 = 310 - 140 = 170 \]

### Step 5: Calculate the Percentage of Profit with Respect to Selling Price
Now, we need to find out what percentage of the selling price the new profit represents:
\[ \text{Percentage of Profit} = \left( \frac{\text{New Profit}}{SP} \right) \times 100 = \left( \frac{170}{310} \right) \times 100 \]

### Step 6: Simplify the Calculation
Calculating the above expression:
\[ \text{Percentage of Profit} = \left( \frac{170 \times 100}{310} \right) = \frac{17000}{310} \]
Now, dividing 17000 by 310:
\[ 17000 \div 310 \approx 54.84 \]

### Step 7: Round to the Nearest Whole Number
Since we need the approximate percentage, we round 54.84 to 55.

### Final Answer
Thus, the approximate percentage of the selling price that will be the profit is **55%**.

---