Amita buys 100 apples at the rate of 12 for Rs 100.80 and 200 apples at the rate of 15 for RS 117. It was found that 10% of the apples were spoilt. She sold all the apples at 20 for Rs 204. Her profit percentage in the entire transaction is:

Options

A. `14.25%`
B. `13.5%`
C. `14.75%`
D. `15.25%`

Answer

To solve the problem step by step, we will calculate the total cost of apples purchased, the total number of apples after accounting for spoilage, the total revenue from selling the apples, and finally, the profit percentage.

### Step 1: Calculate the cost of the first batch of apples
Amita buys 100 apples at the rate of 12 for Rs 100.80.

- Cost of 100 apples = Rs 100.80

### Step 2: Calculate the cost of the second batch of apples
Amita buys 200 apples at the rate of 15 for Rs 117.

- Cost of 200 apples = Rs 117

### Step 3: Calculate the total cost of all apples
Now, we add the costs of both batches:

- Total cost = Cost of first batch + Cost of second batch
- Total cost = Rs 100.80 + Rs 117 = Rs 217.80

### Step 4: Calculate the total number of apples purchased
Total apples purchased = 100 (from the first batch) + 200 (from the second batch) = 300 apples.

### Step 5: Calculate the number of spoiled apples
10% of the apples were spoiled.

- Number of spoiled apples = 10% of 300 = 0.10 × 300 = 30 apples

### Step 6: Calculate the number of good apples
Good apples = Total apples - Spoiled apples
- Good apples = 300 - 30 = 270 apples

### Step 7: Calculate the total revenue from selling the apples
Amita sells all the good apples at the rate of 20 for Rs 204.

- Number of groups of 20 in 270 apples = 270 / 20 = 13.5 (which means she can sell 13 full groups)
- Revenue from 13 groups = 13 × Rs 204 = Rs 2652

### Step 8: Calculate the profit
Profit = Total Revenue - Total Cost
- Profit = Rs 2652 - Rs 217.80 = Rs 2434.20

### Step 9: Calculate the profit percentage
Profit Percentage = (Profit / Total Cost) × 100
- Profit Percentage = (Rs 2434.20 / Rs 217.80) × 100 ≈ 1110.45%

### Final Answer
Amita's profit percentage in the entire transaction is approximately **1110.45%**.

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