Nitesh sells sugar at 20% more than the cost of purchase. He also cheats on weight and weighs only 952 gm/kg of sugar. Giri being a regular customer is offered a discount of 15% and pays only Rs.48 for a kg sugar. The profit of Nitesh when Girl purchases 1 kg of sugar from him is:

Options

A. Rs. 3.60
B. Rs. 3.20
C. Rs. 2.40
D. Rs. 2.70

Answer

To find the profit of Nitesh when Giri purchases 1 kg of sugar from him, we can follow these steps:

### Step 1: Determine the Cost Price (CP) of Sugar
Let the cost price of 1 kg of sugar be \( X \) rupees.

### Step 2: Calculate the Marked Price (MP)
Nitesh sells sugar at 20% more than the cost price. Therefore, the marked price is:
\[ MP = X + 0.2X = 1.2X = \frac{6X}{5} \]

### Step 3: Calculate the Selling Price (SP) after Discount
Giri is offered a discount of 15%. The selling price after the discount can be calculated as:
\[ SP = MP \times \left(1 - \frac{15}{100}\right) = \frac{6X}{5} \times \frac{85}{100} = \frac{6X \times 85}{500} = \frac{510X}{500} = \frac{51X}{50} \]

### Step 4: Set the Selling Price Equal to Rs. 48
According to the problem, Giri pays Rs. 48 for the sugar. Therefore, we can set up the equation:
\[ \frac{51X}{50} = 48 \]

### Step 5: Solve for X
To find \( X \), we can rearrange the equation:
\[ 51X = 48 \times 50 \]
\[ 51X = 2400 \]
\[ X = \frac{2400}{51} \approx 47.06 \text{ rupees} \]

### Step 6: Calculate the Cost Price for 952 grams
Since Nitesh cheats on weight and gives only 952 grams instead of 1000 grams, we need to find the cost price for 952 grams:
\[ \text{CP for 952 grams} = \frac{2400}{51} \times \frac{952}{1000} \]
\[ \text{CP for 952 grams} = \frac{2400 \times 952}{51 \times 1000} \approx \frac{2284800}{51000} \approx 44.8 \text{ rupees} \]

### Step 7: Calculate the Profit
Now, we can calculate the profit made by Nitesh when Giri buys the sugar:
\[ \text{Profit} = SP - CP = 48 - 44.8 = 3.2 \text{ rupees} \]

### Final Answer
Thus, the profit of Nitesh when Giri purchases 1 kg of sugar from him is **Rs. 3.2**.

---