A shopkeeper sold one-third of his goods at a loss of 15%. To get a profit of 10% on the whole transaction, he should sell the remaining articles at a profit of

Options

A. 22 `1/2` %
B. 16 `2/3` %
C. 15%
D. 25%

Answer

To solve the problem step-by-step, we will break down the information given and calculate the required profit percentage for the remaining goods.

### Step 1: Understand the total goods and their selling price
Let’s assume the total cost price (CP) of all the goods is 100 units (this makes calculations simpler).

### Step 2: Calculate the cost price of the sold goods
The shopkeeper sold one-third of his goods, which means:
- Goods sold = 1/3 of total goods = 1/3 of 100 = 33.33 units

### Step 3: Calculate the selling price of the goods sold at a loss
The shopkeeper sold this one-third at a loss of 15%. Therefore, the selling price (SP) of this portion can be calculated as follows:
- Loss = 15% of CP of sold goods = 15% of 33.33 = 5 units
- SP of sold goods = CP of sold goods - Loss = 33.33 - 5 = 28.33 units

### Step 4: Calculate the total cost price of the remaining goods
The remaining goods will be:
- Remaining goods = Total goods - Goods sold = 100 - 33.33 = 66.67 units

### Step 5: Calculate the total selling price required for a 10% profit
To achieve a total profit of 10% on the entire transaction, the total selling price (SP_total) should be:
- Required SP_total = CP_total + Profit = 100 + 10% of 100 = 110 units

### Step 6: Calculate the selling price needed for the remaining goods
Now, we know the selling price of the goods already sold and we can find out how much the remaining goods need to be sold for:
- SP of remaining goods = SP_total - SP of sold goods = 110 - 28.33 = 81.67 units

### Step 7: Calculate the required profit percentage for the remaining goods
Now, we need to find the profit percentage for the remaining goods. The cost price of the remaining goods is 66.67 units, and we need to sell them for 81.67 units.
- Profit = SP of remaining goods - CP of remaining goods = 81.67 - 66.67 = 15 units
- Profit percentage = (Profit / CP of remaining goods) * 100 = (15 / 66.67) * 100 ≈ 22.5%

### Final Answer
The shopkeeper should sell the remaining articles at a profit of approximately **22.5%**.

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