5 kg of butter was bought by a shopkeeper for Rs. 300. One kg become unsaleable. He sells the remaining in such a way that on the whole he occurs a loss of `10%` . At what per kg was the butter sold?

Options

A. Rs . 67.50
B. Rs . 52.50
C. Rs . 60
D. Rs . 72.50

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price of Butter
The shopkeeper bought 5 kg of butter for Rs. 300.

**Cost Price (CP) of 5 kg = Rs. 300**

### Step 2: Calculate the Cost Price per kg
To find the cost price per kg, we divide the total cost price by the total weight of the butter.

\[ \text{Cost Price per kg} = \frac{\text{Total Cost Price}}{\text{Total Weight}} = \frac{300}{5} = Rs. 60 \]

### Step 3: Determine the Weight of Unsold Butter
It is given that 1 kg of butter became unsaleable. Therefore, the remaining butter is:

\[ \text{Remaining Butter} = 5 \text{ kg} - 1 \text{ kg} = 4 \text{ kg} \]

### Step 4: Calculate the Total Cost Price of the Remaining Butter
The cost price of the remaining 4 kg of butter is:

\[ \text{Cost Price of 4 kg} = 4 \text{ kg} \times 60 = Rs. 240 \]

### Step 5: Calculate the Selling Price for a 10% Loss
The shopkeeper incurs a total loss of 10%. Therefore, the selling price (SP) of the remaining butter can be calculated as follows:

\[ \text{Loss} = 10\% \text{ of } 300 = \frac{10}{100} \times 300 = Rs. 30 \]

Thus, the selling price for the entire butter after the loss is:

\[ \text{Selling Price} = \text{Cost Price} - \text{Loss} = 300 - 30 = Rs. 270 \]

### Step 6: Calculate the Selling Price per kg
Now, we need to find the selling price per kg of the remaining 4 kg of butter:

\[ \text{Selling Price per kg} = \frac{\text{Total Selling Price}}{\text{Remaining Weight}} = \frac{270}{4} = Rs. 67.50 \]

### Final Answer
The selling price of butter per kg is Rs. 67.50.

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