Cheap and Best, a kirana shop bought some apples at 4 per rupee and an equal number at 5 per rupee. He then sold the entire quantity at 9 for 2 rupees. What is his percentage profit or loss?

Options

A. `1.25%` loss
B. `6.66%`
C. `8.888%`
D. No profit, no loss

Answer

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

### Step 1: Determine the Cost Price (CP)

1. **Buying Apples:**
- The shop bought apples at two different rates:
- 4 apples for 1 rupee (which means 1 apple costs 0.25 rupees).
- 5 apples for 1 rupee (which means 1 apple costs 0.20 rupees).

2. **Assuming Equal Quantity:**
- Let’s assume the shop bought 20 apples at 4 per rupee and 20 apples at 5 per rupee.
- Therefore, the total quantity of apples bought = 20 + 20 = 40 apples.

3. **Calculating Total Cost:**
- Cost for 20 apples at 4 per rupee = 20 apples * (1 rupee / 4 apples) = 5 rupees.
- Cost for 20 apples at 5 per rupee = 20 apples * (1 rupee / 5 apples) = 4 rupees.
- Total Cost Price (CP) = 5 rupees + 4 rupees = 9 rupees.

### Step 2: Determine the Selling Price (SP)

1. **Selling Rate:**
- The shop sells apples at 9 apples for 2 rupees.

2. **Calculating Total Selling Price for 40 Apples:**
- To find out how much he earns from selling 40 apples, we first find out how many sets of 9 apples are in 40.
- The least common multiple (LCM) of 9 and 40 is 360.
- Therefore, we need to calculate how many times 9 fits into 360:
- Number of sets of 9 in 360 = 360 / 9 = 40 sets.
- Selling Price for 40 sets (360 apples) = (360 / 9) * 2 = 80 rupees.

### Step 3: Calculate Profit or Loss

1. **Finding Profit or Loss:**
- Total Cost Price (CP) for 360 apples = 81 rupees (from the previous calculation).
- Total Selling Price (SP) for 360 apples = 80 rupees.
- Since SP < CP, there is a loss.
- Loss = CP - SP = 81 rupees - 80 rupees = 1 rupee.

### Step 4: Calculate Percentage Loss

1. **Percentage Loss Formula:**
- Percentage Loss = (Loss / CP) * 100
- Percentage Loss = (1 / 81) * 100 = 1.25%.

### Final Answer:
The percentage loss incurred by the shop is **1.25%**.

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