Anu fixes the selling price of an article at 25% above its cost of production. If the cost of production goes up by 20% and she raises the selling price by 10% then her percentage profit is (correct to one decimal place):

Options

A. 0.146
B. 0.138
C. 0.152
D. 0.164

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Assume the Cost of Production
Let's assume the cost of production (CP) of the article is \(100\) (this simplifies calculations).

### Step 2: Calculate the Initial Selling Price
Anu fixes the selling price (SP) at 25% above the cost of production.
\[ SP = CP + 25\% \text{ of } CP = 100 + 0.25 \times 100 = 100 + 25 = 125 \]

### Step 3: Adjust the Cost of Production
The cost of production increases by 20%.
\[ \text{New CP} = CP + 20\% \text{ of } CP = 100 + 0.20 \times 100 = 100 + 20 = 120 \]

### Step 4: Adjust the Selling Price
The selling price is raised by 10%.
\[ \text{New SP} = SP + 10\% \text{ of } SP = 125 + 0.10 \times 125 = 125 + 12.5 = 137.5 \]

### Step 5: Calculate the Profit
Profit is calculated as the difference between the new selling price and the new cost price.
\[ \text{Profit} = \text{New SP} - \text{New CP} = 137.5 - 120 = 17.5 \]

### Step 6: Calculate the Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{New CP}} \right) \times 100 = \left( \frac{17.5}{120} \right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = \frac{17.5 \times 100}{120} = \frac{1750}{120} \approx 14.5833 \]

### Step 7: Round to One Decimal Place
Rounding \(14.5833\) to one decimal place gives:
\[ \text{Profit Percentage} \approx 14.6 \]

Thus, the final answer is:
\[ \text{Percentage profit is } 14.6\% \]