A shopkeeper marks every item available in his shop at 20% higher than the actual cost price. He offers a discount of 10% on every item. If an item is sold for 35,400, find his profit percentage.

Options

A. 0.04
B. 0.08
C. 0.066
D. 0.15

Answer

To solve the problem step by step, we will first identify the cost price, then calculate the marked price, apply the discount, and finally determine the profit percentage.

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

### Step 2: Calculate the Marked Price (MP)
The shopkeeper marks every item at 20% higher than the cost price. Therefore, the marked price (MP) can be calculated as:
\[ MP = CP + 20\% \text{ of } CP = x + 0.2x = 1.2x \]

### Step 3: Calculate the Selling Price (SP) after Discount
The shopkeeper offers a discount of 10% on the marked price. Thus, the selling price (SP) after the discount can be calculated as:
\[ SP = MP - 10\% \text{ of } MP = MP - 0.1 \times MP = 0.9 \times MP \]
Substituting the value of MP from Step 2:
\[ SP = 0.9 \times 1.2x = 1.08x \]

### Step 4: Set the Selling Price Equal to the Given Value
According to the problem, the selling price is given as Rs. 35,400. Therefore, we can set up the equation:
\[ 1.08x = 35400 \]

### Step 5: Solve for the Cost Price (CP)
To find the cost price \( x \), we can rearrange the equation:
\[ x = \frac{35400}{1.08} \]
Calculating this gives:
\[ x = 32777.78 \text{ (approximately)} \]

### Step 6: Calculate the Profit
Now we can calculate the profit. The profit is given by:
\[ \text{Profit} = SP - CP = 35400 - 32777.78 = 2622.22 \text{ (approximately)} \]

### Step 7: Calculate the Profit Percentage
Profit percentage can be calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{2622.22}{32777.78} \right) \times 100 \approx 8\% \]

### Final Answer
The profit percentage is approximately **8%**.

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