Rajaram purchased a certain amount of wheat. If he sold one-fourth of the wheat at a profit of 12%, then the profit percent he needs to make on the remaining wheat to make an overall profit of 15% is:

Options

A. `18%`
B. `16%`
C. `15%`
D. `20%`

Answer

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

### Step 1: Understand the total amount of wheat
Let's assume Rajaram purchased a total of 4 units of wheat. This is a convenient number that makes calculations easier.

### Step 2: Calculate the amount of wheat sold
Rajaram sold one-fourth of the wheat. Therefore, the amount of wheat sold is:
\[ \text{Wheat sold} = \frac{1}{4} \times 4 = 1 \text{ unit} \]

### Step 3: Calculate the profit from the sold wheat
Rajaram sold this 1 unit of wheat at a profit of 12%. The profit from this sale can be calculated as follows:
\[ \text{Profit from sold wheat} = 12\% \text{ of cost price of 1 unit} \]
If we assume the cost price of 1 unit of wheat is \(C\), then:
\[ \text{Profit from sold wheat} = 0.12C \]

### Step 4: Calculate the total cost price of the wheat
The total cost price of the 4 units of wheat is:
\[ \text{Total cost price} = 4C \]

### Step 5: Calculate the desired overall profit
Rajaram wants to make an overall profit of 15% on the total cost price. Therefore, the total selling price needed to achieve this profit is:
\[ \text{Total selling price} = \text{Total cost price} + 15\% \text{ of Total cost price} \]
\[ \text{Total selling price} = 4C + 0.15 \times 4C = 4C + 0.6C = 4.6C \]

### Step 6: Calculate the selling price of the remaining wheat
The selling price of the 1 unit of wheat sold at a profit of 12% is:
\[ \text{Selling price of sold wheat} = C + 0.12C = 1.12C \]

### Step 7: Calculate the selling price needed from the remaining wheat
The selling price needed from the remaining 3 units of wheat to achieve the overall profit is:
\[ \text{Selling price from remaining wheat} = \text{Total selling price} - \text{Selling price of sold wheat} \]
\[ \text{Selling price from remaining wheat} = 4.6C - 1.12C = 3.48C \]

### Step 8: Calculate the required profit percent on the remaining wheat
The cost price of the remaining 3 units of wheat is:
\[ \text{Cost price of remaining wheat} = 3C \]
To find the required profit percent on the remaining wheat, we first find the profit:
\[ \text{Profit from remaining wheat} = \text{Selling price from remaining wheat} - \text{Cost price of remaining wheat} \]
\[ \text{Profit from remaining wheat} = 3.48C - 3C = 0.48C \]
Now, the profit percent is given by:
\[ \text{Profit percent} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 = \left(\frac{0.48C}{3C}\right) \times 100 = \frac{0.48}{3} \times 100 = 16\% \]

### Final Answer
The profit percent Rajaram needs to make on the remaining wheat to achieve an overall profit of 15% is **16%**.