`200` kg of sugar was purchased at the rate of `"Rs. 15"` per kg and sold at a profit of `5%`. Compute the profit and the selling price per kg.

Options

A. 15.75
B. 16.75
C. 17.75
D. 18.75

Answer

To solve the problem step by step, we will calculate the cost price, profit, and selling price per kg of sugar.

### Step 1: Calculate the Cost Price (CP)
The cost price of sugar is given as Rs. 15 per kg. For 200 kg, the total cost price (CP) can be calculated as:

\[ \text{CP} = \text{Cost per kg} \times \text{Quantity} \]
\[ \text{CP} = 15 \, \text{Rs/kg} \times 200 \, \text{kg} = 3000 \, \text{Rs} \]

### Step 2: Calculate the Profit
The profit percentage is given as 5%. To find the profit in Rs., we can use the formula:

\[ \text{Profit} = \left(\frac{\text{Profit Percentage}}{100}\right) \times \text{CP} \]
Substituting the values:

\[ \text{Profit} = \left(\frac{5}{100}\right) \times 3000 = 150 \, \text{Rs} \]

### Step 3: Calculate the Selling Price (SP)
The selling price can be calculated using the formula:

\[ \text{SP} = \text{CP} + \text{Profit} \]
Substituting the values:

\[ \text{SP} = 3000 + 150 = 3150 \, \text{Rs} \]

### Step 4: Calculate the Selling Price per kg
To find the selling price per kg, we divide the total selling price by the quantity:

\[ \text{Selling Price per kg} = \frac{\text{SP}}{\text{Quantity}} \]
Substituting the values:

\[ \text{Selling Price per kg} = \frac{3150}{200} = 15.75 \, \text{Rs/kg} \]

### Summary of Results
- Profit = Rs. 150
- Selling Price per kg = Rs. 15.75