For an article the profit is 190% of the cost price. If the cost price increases by 10% but the selling price remains same, then profit is what percentage of selling price (approximately) ?

Options

A. 54
B. 62
C. 70
D. 163

Answer

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

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \( CP = 100x \).

### Step 2: Calculate the Profit
The profit is given as 190% of the cost price. Therefore,
\[ \text{Profit} = 190\% \text{ of } CP = 190\% \times 100x = \frac{190}{100} \times 100x = 190x. \]

### Step 3: Calculate the Selling Price
The selling price (SP) can be calculated as:
\[ SP = CP + \text{Profit} = 100x + 190x = 290x. \]

### Step 4: Increase the Cost Price by 10%
Now, if the cost price increases by 10%, the new cost price (CP') will be:
\[ CP' = CP + 10\% \text{ of } CP = 100x + 10\% \times 100x = 100x + 10x = 110x. \]

### Step 5: Calculate the New Profit
The new profit (Profit') is calculated using the new cost price:
\[ \text{Profit'} = SP - CP' = 290x - 110x = 180x. \]

### Step 6: Calculate the Profit Percentage
To find the profit as a percentage of the selling price, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit'}}{SP} \right) \times 100 = \left( \frac{180x}{290x} \right) \times 100. \]
Here, \( x \) cancels out:
\[ \text{Profit Percentage} = \left( \frac{180}{290} \right) \times 100. \]

### Step 7: Simplify the Calculation
Now, simplifying \( \frac{180}{290} \):
\[ \frac{180}{290} = \frac{18}{29}. \]
Now, multiplying by 100:
\[ \text{Profit Percentage} = \frac{18}{29} \times 100 \approx 62.07\%. \]

Thus, the profit is approximately **62%** of the selling price.