A man purchases some oranges at the rate of 3 for Rs 40 and the same quantity at 5 for 60. If he sells all the oranges at the rate of 3 for 50, find his gain or loss percent (to the nearest integer).

Options

A. a)31% profit
B. b)34% loss
C. c)31% loss
D. d)32%profit

Answer

To solve the problem step by step, we will first calculate the cost price (CP) of the oranges and then the selling price (SP) before finding the profit or loss percentage.

### Step 1: Calculate the total cost price (CP) of the oranges.

1. **Purchase the first quantity of oranges:**
- Rate: 3 oranges for Rs 40
- Cost per orange = 40 / 3 = Rs 13.33 (approximately)

Let's assume he buys 15 oranges (to make calculations easier).
- Number of oranges purchased = 15
- Total cost for 15 oranges = (15 / 3) * 40 = 5 * 40 = Rs 200

2. **Purchase the second quantity of oranges:**
- Rate: 5 oranges for Rs 60
- Cost per orange = 60 / 5 = Rs 12

Again, he buys 15 oranges.
- Total cost for 15 oranges = (15 / 5) * 60 = 3 * 60 = Rs 180

3. **Total cost price (CP) of all oranges:**
- Total CP = Cost of first quantity + Cost of second quantity
- Total CP = 200 + 180 = Rs 380

### Step 2: Calculate the total selling price (SP) of the oranges.

1. **Selling price of oranges:**
- Rate: 3 oranges for Rs 50
- Selling price per orange = 50 / 3 = Rs 16.67 (approximately)

He has a total of 30 oranges (15 from each purchase).
- Total SP for 30 oranges = (30 / 3) * 50 = 10 * 50 = Rs 500

### Step 3: Calculate profit or loss.

1. **Profit = Selling Price - Cost Price**
- Profit = SP - CP
- Profit = 500 - 380 = Rs 120

### Step 4: Calculate profit percentage.

1. **Profit Percentage = (Profit / Cost Price) * 100**
- Profit Percentage = (120 / 380) * 100
- Profit Percentage = 31.57% (approximately)

### Step 5: Round to the nearest integer.

1. **Final Profit Percentage:**
- Rounding 31.57% gives us 32%.

### Final Answer:
The gain percent is **32%**.

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