A retailer purchased 50 kg of a vegetable from a wholesale market. He sold half of it at a profit of Rs. 450, and the rest at a loss of Rs. 275. What was the difference (in Rs) between the two selling prices per kg of the vegetable?

Options

A. 29
B. 18
C. 7
D. 12

Answer

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

### Step 1: Define the variables
Let the cost price of 1 kg of the vegetable be Rs. X.

### Step 2: Calculate the cost price for half of the vegetable
Since the retailer purchased 50 kg of the vegetable, half of it is 25 kg. Therefore, the cost price for 25 kg is:
\[ \text{Cost Price for 25 kg} = 25 \times X = 25X \]

### Step 3: Calculate the selling price for the first half
The retailer sold the first half (25 kg) at a profit of Rs. 450. Thus, the selling price for this half is:
\[ \text{Selling Price for 25 kg} = \text{Cost Price} + \text{Profit} = 25X + 450 \]
To find the selling price per kg, we divide by 25:
\[ \text{Selling Price per kg for first half} = \frac{25X + 450}{25} = X + 18 \]

### Step 4: Calculate the cost price for the second half
The cost price for the remaining half (another 25 kg) is again:
\[ \text{Cost Price for 25 kg} = 25X \]

### Step 5: Calculate the selling price for the second half
The retailer sold the second half (25 kg) at a loss of Rs. 275. Thus, the selling price for this half is:
\[ \text{Selling Price for 25 kg} = \text{Cost Price} - \text{Loss} = 25X - 275 \]
To find the selling price per kg, we divide by 25:
\[ \text{Selling Price per kg for second half} = \frac{25X - 275}{25} = X - 11 \]

### Step 6: Calculate the difference between the two selling prices
Now we need to find the difference between the two selling prices per kg:
\[ \text{Difference} = \left( X + 18 \right) - \left( X - 11 \right) \]
Simplifying this gives:
\[ \text{Difference} = X + 18 - X + 11 = 29 \]

### Conclusion
The difference between the two selling prices per kg of the vegetable is Rs. 29.

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