A vegetable vendor buys 240 kg of onions for Rs. 380. If 20% of the onion is unusable, at what average price per kilogram must he sell the rest of the onions in order to make a profit of 25%?

Options

A. Rs. 2.47
B. Rs. 3.50
C. Rs. 2.10
D. Rs. 1.47

Answer

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

### Step 1: Calculate the cost price per kilogram of onions.
The vendor buys 240 kg of onions for Rs. 380.

\[ \text{Cost price per kg} = \frac{\text{Total Cost}}{\text{Total Weight}} = \frac{380}{240} \]

Calculating this gives:

\[ \text{Cost price per kg} = \frac{380}{240} = \frac{19}{12} \approx 1.58 \text{ Rs/kg} \]

### Step 2: Determine the usable quantity of onions.
20% of the onions are unusable, which means 80% are usable.

\[ \text{Usable onions} = 240 \times \frac{80}{100} = 240 \times 0.8 = 192 \text{ kg} \]

### Step 3: Calculate the desired selling price to achieve a 25% profit.
To find the selling price that gives a 25% profit, we first calculate the total cost of the onions:

\[ \text{Total Cost} = 380 \text{ Rs} \]

Now, we calculate the profit:

\[ \text{Profit} = 25\% \text{ of Total Cost} = \frac{25}{100} \times 380 = 95 \text{ Rs} \]

Now, the total amount he needs to earn to achieve this profit is:

\[ \text{Total Selling Price} = \text{Total Cost} + \text{Profit} = 380 + 95 = 475 \text{ Rs} \]

### Step 4: Calculate the average selling price per kilogram of usable onions.
Now, we need to find the average price per kilogram of the usable onions:

\[ \text{Average Selling Price per kg} = \frac{\text{Total Selling Price}}{\text{Usable Quantity}} = \frac{475}{192} \]

Calculating this gives:

\[ \text{Average Selling Price per kg} \approx 2.47 \text{ Rs/kg} \]

### Final Answer:
The average price per kilogram at which the vendor must sell the usable onions to make a profit of 25% is approximately **Rs. 2.47**.

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