By selling 12 kg of potatoes for Rs. 63, a shopkeeper gains 5%.What does he gain or lose per cent by selling 50 kg of the same potatoes for Rs. 247.50 ?

Options

A. 1%loss
B. No profit, no loss
C. 2.5%loss
D. 1%profit

Answer

To solve the problem step-by-step, we will first find the cost price of the potatoes and then determine the gain or loss percentage when selling 50 kg of potatoes for Rs. 247.50.

### Step 1: Find the Cost Price (CP) of 12 kg of Potatoes
Given that the selling price (SP) of 12 kg of potatoes is Rs. 63 and the shopkeeper gains 5%, we can use the formula for selling price:

\[ SP = CP + \text{Gain} \]

Where Gain can be calculated as:

\[ \text{Gain} = \frac{\text{Gain%}}{100} \times CP \]

Let the cost price of 12 kg of potatoes be \( CP \).

Since the gain is 5%, we can express the selling price as:

\[ 63 = CP + \frac{5}{100} \times CP \]

This simplifies to:

\[ 63 = CP \left(1 + \frac{5}{100}\right) = CP \left(\frac{105}{100}\right) \]

Now, we can solve for \( CP \):

\[ CP = \frac{63 \times 100}{105} = \frac{6300}{105} = 60 \]

### Step 2: Find the Cost Price (CP) of 1 kg of Potatoes
Now that we know the cost price of 12 kg of potatoes is Rs. 60, we can find the cost price of 1 kg:

\[ CP \text{ (per kg)} = \frac{60}{12} = 5 \]

### Step 3: Find the Selling Price (SP) of 50 kg of Potatoes
The shopkeeper sells 50 kg of potatoes for Rs. 247.50. We need to find the selling price per kg:

\[ SP \text{ (per kg)} = \frac{247.50}{50} = 4.95 \]

### Step 4: Determine Gain or Loss
Now we compare the selling price per kg with the cost price per kg:

- Cost Price per kg = Rs. 5
- Selling Price per kg = Rs. 4.95

Since the selling price is less than the cost price, the shopkeeper incurs a loss.

### Step 5: Calculate the Loss Amount
The loss per kg can be calculated as:

\[ \text{Loss} = CP - SP = 5 - 4.95 = 0.05 \]

### Step 6: Calculate the Loss Percentage
To find the loss percentage, we use the formula:

\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 \]

Substituting the values:

\[ \text{Loss Percentage} = \left(\frac{0.05}{5}\right) \times 100 = 1\% \]

### Final Answer
The shopkeeper incurs a loss of **1%** when selling 50 kg of potatoes for Rs. 247.50.

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