A fruit merchant bought some oranges at the rate of 4 for Rs 10 and same amount of oranges at the rate of 5 for Rs 10 . If he sells whole stock at the rate of 9 for Rs 20. Find his profit /loss %.

Answer

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

### Step 1: Determine the cost price of the oranges

1. **Calculate the cost of the first batch of oranges:**
- The merchant bought oranges at the rate of 4 for Rs 10.
- Therefore, the cost of one orange = Rs 10 / 4 = Rs 2.5.

2. **Calculate the cost of the second batch of oranges:**
- The merchant bought oranges at the rate of 5 for Rs 10.
- Therefore, the cost of one orange = Rs 10 / 5 = Rs 2.

### Step 2: Find the total number of oranges purchased

3. **Let’s assume the merchant bought 'x' oranges at each rate.**
- For the first batch:
- If he bought 'x' oranges, the number of sets of 4 oranges he bought = x / 4.
- Therefore, the total cost for the first batch = (x / 4) * 10 = (10x / 4) = Rs (2.5x).

- For the second batch:
- The number of sets of 5 oranges he bought = x / 5.
- Therefore, the total cost for the second batch = (x / 5) * 10 = (10x / 5) = Rs (2x).

### Step 3: Calculate the total cost price

4. **Total cost price (CP) of oranges:**
- Total CP = Cost of first batch + Cost of second batch
- Total CP = Rs (2.5x + 2x) = Rs (4.5x).

### Step 4: Calculate the selling price of the oranges

5. **Selling price of the whole stock:**
- The merchant sells the oranges at the rate of 9 for Rs 20.
- Therefore, the selling price of one orange = Rs 20 / 9.

6. **Total selling price (SP) of '2x' oranges:**
- Total SP = (Number of oranges sold) * (Selling price per orange)
- Total SP = (2x) * (20 / 9) = Rs (40x / 9).

### Step 5: Calculate profit or loss

7. **Profit or Loss Calculation:**
- Profit or Loss = Total SP - Total CP
- Profit or Loss = (40x / 9) - (4.5x).

### Step 6: Find the profit or loss percentage

8. **To find the profit or loss percentage:**
- Profit or Loss % = [(Profit or Loss) / Total CP] * 100
- Substitute the values:
- Profit or Loss % = [((40x / 9) - (4.5x)) / (4.5x)] * 100.

### Step 7: Simplify the expression

9. **Simplifying the expression:**
- Convert 4.5x to a fraction with a common denominator:
- 4.5x = (40.5x / 9).
- Now, the equation becomes:
- Profit or Loss % = [((40x / 9) - (40.5x / 9)) / (4.5x)] * 100
- = [(-0.5x / 9) / (4.5x)] * 100
- = [(-0.5 / 9 * 1 / 4.5)] * 100
- = [-0.5 / 40.5] * 100
- = -1.2345679%.

### Conclusion

The merchant incurs a loss of approximately **1.23%**.