A frult-seller buys some oranges and by selling 40% of them he realises the cost price of all the oranges. As the oranges being to grow over-ripe, he reduces the price and sells 80% of the re maining oranges at half the pre vious rate of profit. The rest of the oranges being rotten are thrown away. The overall per centage of profit is

Options

A. (A) 80
B. (B) 84
C. (C) 94
D. (D) 96

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Initial Purchase
Assume the fruit seller buys 100 oranges at a cost price of 1 rupee each.
- **Total Cost Price (CP)** = 100 oranges × 1 rupee/orange = 100 rupees.

### Step 2: Selling 40% of the Oranges
The seller sells 40% of the oranges to recover the cost price.
- **Number of oranges sold** = 40% of 100 = 40 oranges.
- The selling price (SP) of these 40 oranges is equal to the total cost price of all oranges, which is 100 rupees.

### Step 3: Remaining Oranges After First Sale
After selling 40 oranges, the remaining oranges are:
- **Remaining oranges** = 100 - 40 = 60 oranges.

### Step 4: Selling 80% of the Remaining Oranges
The seller now sells 80% of the remaining 60 oranges at half the previous rate of profit.
- **Number of oranges sold now** = 80% of 60 = 48 oranges.

### Step 5: Calculate the Selling Price of the Remaining Oranges
First, we need to find the profit percentage from the first sale to determine the selling price for the second sale.
- The SP of the 40 oranges sold initially = 100 rupees (which is the total cost price).
- **Profit from the first sale** = SP - CP = 100 - 40 = 60 rupees.
- **Profit percentage** = (Profit/CP) × 100 = (60/40) × 100 = 150%.

Now, since the seller sells the remaining oranges at half the previous rate of profit:
- **New profit percentage** = 150% / 2 = 75%.

### Step 6: Calculate the Selling Price of 48 Oranges
The cost price of the remaining 48 oranges:
- **Cost Price of 48 oranges** = (CP of 60 oranges / 60) × 48 = (40 rupees / 60) × 48 = 32 rupees.

Now, calculate the selling price using the new profit percentage:
- **Selling Price (SP) of 48 oranges** = CP + Profit
- Profit = 75% of CP = (75/100) × 32 = 24 rupees.
- **SP of 48 oranges** = 32 + 24 = 56 rupees.

### Step 7: Total Selling Price and Profit Calculation
Now, we calculate the total selling price and total profit:
- **Total SP** = SP from first sale + SP from second sale = 100 + 56 = 156 rupees.
- **Total Profit** = Total SP - Total CP = 156 - 100 = 56 rupees.

### Step 8: Calculate Overall Percentage of Profit
Finally, calculate the overall percentage of profit:
- **Overall Profit Percentage** = (Total Profit / Total CP) × 100 = (56 / 100) × 100 = 56%.

### Final Answer
The overall percentage of profit is **56%**.

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