A man buys a certain number of oranges at 20 for 60 and an equal number at 30 for 60. He mixes them and sells them at 25 for 60. What is gain or loss per cent?

Options

A. Gain of 4%
B. Loss of4%
C. Neither gain nor loss
D. Loss of5%

Answer

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

### Step 1: Calculate the Cost Price of Oranges
The man buys oranges in two batches:
1. **First Batch**: 20 oranges for 60 rupees.
- Cost Price (CP1) for 20 oranges = 60 rupees
- Therefore, Cost Price for 1 orange = 60 / 20 = 3 rupees

2. **Second Batch**: 30 oranges for 60 rupees.
- Cost Price (CP2) for 30 oranges = 60 rupees
- Therefore, Cost Price for 1 orange = 60 / 30 = 2 rupees

### Step 2: Calculate Total Cost Price for Equal Number of Oranges
Since he buys an equal number of oranges from both batches, let's find out how many oranges he has in total.

- Let’s assume he buys 60 oranges from each batch (to make calculations easier).
- Total Cost Price for 60 oranges from the first batch = 60 / 20 * 60 = 180 rupees
- Total Cost Price for 60 oranges from the second batch = 60 / 30 * 60 = 120 rupees

### Step 3: Calculate Total Cost Price
Total Cost Price (CP) for 120 oranges:
- CP = CP1 + CP2 = 180 + 120 = 300 rupees

### Step 4: Calculate Selling Price
The man sells the mixed oranges at 25 for 60 rupees.
- Selling Price (SP) for 25 oranges = 60 rupees
- Therefore, Selling Price for 1 orange = 60 / 25 = 2.4 rupees

Now, for 120 oranges:
- Total Selling Price = 120 * (60 / 25) = 120 * 2.4 = 288 rupees

### Step 5: Calculate Gain or Loss
Now, we can find out if there is a gain or loss:
- Total Cost Price = 300 rupees
- Total Selling Price = 288 rupees

Loss = CP - SP = 300 - 288 = 12 rupees

### Step 6: Calculate Loss Percentage
To find the loss percentage:
- Loss Percentage = (Loss / Cost Price) * 100
- Loss Percentage = (12 / 300) * 100 = 4%

### Final Answer
The man incurs a loss of 4%.

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