A merchant bought some goods worth Rs. 6000 and sold half of them at 12% profit . At what profit per cent should sell the remaining goods to make and overall profit of 18%?

Options

A. 24
B. 28
C. 18
D. 20

Explanation

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

### Step 1: Calculate the cost of goods sold and the profit from the first half.
The merchant bought goods worth Rs. 6000. He sold half of them, which is Rs. 3000, at a profit of 12%.

**Calculation:**
Profit from the first half = 12% of Rs. 3000
= (12/100) * 3000
= Rs. 360

### Step 2: Calculate the total profit desired for the entire amount.
The merchant wants an overall profit of 18% on the total cost of Rs. 6000.

**Calculation:**
Total desired profit = 18% of Rs. 6000
= (18/100) * 6000
= Rs. 1080

### Step 3: Determine the profit needed from the second half of the goods.
Now, we need to find out how much profit is needed from the remaining half of the goods (also worth Rs. 3000) to achieve the overall profit of Rs. 1080.

**Calculation:**
Profit needed from the second half = Total desired profit - Profit from the first half
= Rs. 1080 - Rs. 360
= Rs. 720

### Step 4: Calculate the required profit percentage on the second half.
Now, we need to find out what percentage of profit this Rs. 720 represents on the remaining Rs. 3000.

**Calculation:**
Let the required profit percentage be X%.
Profit = (X/100) * 3000
Setting this equal to the profit needed from the second half, we have:
(X/100) * 3000 = 720

### Step 5: Solve for X.
To find X, we rearrange the equation:

**Calculation:**
X = (720 * 100) / 3000
= 72000 / 3000
= 24%

Thus, the merchant should sell the remaining goods at a profit percentage of **24%** to achieve an overall profit of 18%.

### Final Answer:
The profit percentage required on the remaining goods is **24%**.

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