A merchant earns a profit of 20% by selling a basket containing 80 apples whose cost is Rs. 240 but he gives one- fourth of it to his friend at cost price and sells the remaining apples. In order to earn the same profit,at what price must he sell each apple?

Options

A. X3.00
B. X3.60
C. X3.80
D. X4.80

Answer

To solve the problem step by step, we will follow the details provided in the question.

### Step 1: Calculate the total cost price of the basket of apples.
The cost price of the basket containing 80 apples is given as Rs. 240.

### Step 2: Calculate the selling price for a 20% profit.
To find the selling price (SP) when the profit is 20%, we use the formula:
\[ SP = CP + (Profit \% \times CP) \]
Where CP is the cost price.

Calculating the selling price:
\[ SP = 240 + (20\% \times 240) = 240 + (0.20 \times 240) = 240 + 48 = 288 \]

### Step 3: Determine how many apples the merchant gives to his friend.
The merchant gives one-fourth of the apples to his friend.
Calculating one-fourth of 80 apples:
\[ \text{Apples given to friend} = \frac{1}{4} \times 80 = 20 \text{ apples} \]

### Step 4: Calculate the number of apples remaining.
After giving away 20 apples, the number of apples remaining with the merchant is:
\[ \text{Remaining apples} = 80 - 20 = 60 \text{ apples} \]

### Step 5: Calculate the cost price of the apples given to the friend.
The cost price of the 20 apples given to the friend is:
\[ \text{Cost price of 20 apples} = \frac{240}{80} \times 20 = 3 \times 20 = 60 \text{ Rs.} \]

### Step 6: Calculate the selling price of the apples given to the friend.
The merchant sells the 20 apples to his friend at cost price, which is Rs. 60.

### Step 7: Calculate the total selling price needed to maintain the same profit.
Since the total selling price for the entire basket to achieve a 20% profit is Rs. 288, and he has already made Rs. 60 from selling the 20 apples, the remaining selling price needed from the 60 apples is:
\[ \text{Remaining SP} = 288 - 60 = 228 \text{ Rs.} \]

### Step 8: Calculate the selling price per apple for the remaining apples.
To find the selling price per apple for the remaining 60 apples:
\[ \text{Selling price per apple} = \frac{228}{60} = 3.8 \text{ Rs.} \]

### Conclusion:
The merchant must sell each of the remaining apples at Rs. 3.8 to earn the same profit.

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