A trader bought 10 kg of apples for 405 out of which 1 kg of apples were found to be rotten. If he wishes to make a profit of 10%, at what rate should he sell the remaining apples per kg?

Options

A. 45
B. 49.5
C. 50
D. 51

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the cost price (CP) of the apples.
The trader bought 10 kg of apples for 405.

**Cost Price (CP) = 405**

### Step 2: Calculate the profit desired.
The trader wishes to make a profit of 10%.

**Profit = 10% of CP = 10/100 × 405 = 40.5**

### Step 3: Calculate the total selling price (SP) required to achieve the desired profit.
To find the selling price, we add the profit to the cost price.

**Selling Price (SP) = CP + Profit = 405 + 40.5 = 445.5**

### Step 4: Determine the quantity of good apples available for sale.
Since 1 kg of apples was found to be rotten, the remaining quantity is:

**Remaining apples = 10 kg - 1 kg = 9 kg**

### Step 5: Calculate the selling price per kg of the remaining apples.
To find the selling price per kg, we divide the total selling price by the quantity of good apples.

**Selling Price per kg = Total SP / Remaining quantity = 445.5 / 9**

Calculating this gives:

**Selling Price per kg = 49.5**

### Final Answer:
The trader should sell the remaining apples at **49.5 per kg** to achieve a profit of 10%.

---