A man purchases some mangoes at the rate of 3 for 4 and the same quantity at 5 for 6. If he sells all the mangoes at the rate of 3 for 5, find his approximate gain or loss per cent.

Options

A. 35%loss
B. 32%loss
C. 32%profit
D. 35%gain

Answer

To solve the problem step by step, we will calculate the cost price and selling price of the mangoes, and then find the gain or loss percentage.

### Step 1: Calculate the Cost Price of Mangoes
1. **Purchasing Mangoes at Rate 3 for 4:**
- Cost Price (CP) for 3 mangoes = 4
- Therefore, CP for 1 mango = 4 / 3 = 1.33 (approximately)

2. **Purchasing Mangoes at Rate 5 for 6:**
- Cost Price (CP) for 5 mangoes = 6
- Therefore, CP for 1 mango = 6 / 5 = 1.20

3. **Assuming he purchases the same quantity of mangoes in both cases:**
- Let’s assume he buys 15 mangoes in total (i.e., 7.5 mangoes from each rate).
- From the first rate (3 for 4), he buys 7.5 mangoes:
- Cost = (7.5 / 3) * 4 = 10
- From the second rate (5 for 6), he buys 7.5 mangoes:
- Cost = (7.5 / 5) * 6 = 9

4. **Total Cost Price (CP):**
- Total CP = 10 + 9 = 19

### Step 2: Calculate the Selling Price of Mangoes
1. **Selling Mangoes at Rate 3 for 5:**
- Selling Price (SP) for 3 mangoes = 5
- Therefore, SP for 1 mango = 5 / 3 = 1.67 (approximately)

2. **Total Selling Price for 15 mangoes:**
- SP for 15 mangoes = (15 / 3) * 5 = 25

### Step 3: Calculate Gain or Loss
1. **Gain or Loss Calculation:**
- Gain = Selling Price - Cost Price
- Gain = 25 - 19 = 6

### Step 4: Calculate Gain Percentage
1. **Gain Percentage Formula:**
- Gain Percentage = (Gain / Cost Price) * 100
- Gain Percentage = (6 / 19) * 100 ≈ 31.58%

### Step 5: Conclusion
- The approximate gain percentage is **32%**.