A shopkeeper purchased some oranges. By selling 40% oranges he got his purchasing price and sold 80% of remaining at the half of the profit % earlier and thrown away rest oranges. Find profit %.

Answer

To solve the problem step by step, we can break it down as follows:

### Step 1: Understand the Purchase
The shopkeeper purchased 100 oranges for 100 INR.

### Step 2: Calculate the Selling Price of the First Batch
He sold 40% of the oranges.
- Number of oranges sold = 40% of 100 = 40 oranges.
- Selling price for these 40 oranges = 100 INR (which is equal to the cost price).

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

### Step 4: Calculate the Selling Price of the Second Batch
He sold 80% of the remaining oranges.
- Number of oranges sold = 80% of 60 = 48 oranges.

### Step 5: Determine the Profit Percentage from the First Sale
From the first sale, he sold 40 oranges for 100 INR, which means:
- Cost price of 40 oranges = 40 INR (since 100 INR for 100 oranges).
- Profit from the first sale = Selling Price - Cost Price = 100 - 40 = 60 INR.
- Profit percentage = (Profit/Cost Price) * 100 = (60/40) * 100 = 150%.

### Step 6: Calculate the Selling Price of the Second Batch
The profit percentage on the first batch was 150%. The shopkeeper sold the second batch at half of this profit percentage:
- Half of 150% = 75%.
- Selling price for the second batch = Cost Price of 48 oranges + Profit.
- Cost Price of 48 oranges = (48/100) * 100 = 48 INR.
- Profit on 48 oranges = 75% of 48 = (75/100) * 48 = 36 INR.
- Selling Price for 48 oranges = Cost Price + Profit = 48 + 36 = 84 INR.

### Step 7: Calculate Total Selling Price
The total selling price from both transactions:
- Total Selling Price = Selling Price from first batch + Selling Price from second batch = 100 + 84 = 184 INR.

### Step 8: Calculate Total Profit
Total Cost Price of all oranges = 100 INR.
Total Profit = Total Selling Price - Total Cost Price = 184 - 100 = 84 INR.

### Step 9: Calculate Overall Profit Percentage
Profit Percentage = (Total Profit / Total Cost Price) * 100 = (84 / 100) * 100 = 84%.

### Final Answer
The profit percentage is **84%**.

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