Question

A trader bought 10 kg of apples for 405 out of which 1 kg of apples were found to be rotten. If he wishes to make a profit of 10%, at what rate should he sell the remaining apples per kg?

• A. 45
• B. 49.50
• C. 50
• D. 51

Hint:

Always ensure to account for spoiled or unavailable goods when calculating the selling price per unit. The profit percentage is typically calculated on the cost price (CP). Work step-by-step to avoid errors.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem involves calculating the selling price per kg for a trader to achieve a certain profit margin, after some goods have been spoiled.

Step 2: Key Formula or Approach:
1. Calculate the total cost price.
2. Calculate the desired selling price to achieve the target profit.
3. Adjust the quantity of goods available for sale.
4. Calculate the selling price per unit of the remaining goods.

Step 3: Detailed Explanation:
1. Total Cost Price (CP):
The trader bought 10 kg of apples for Rs. 405.
So, CP = Rs. 405.
2. Apples available for sale:
Total apples bought = 10 kg.
Rotten apples = 1 kg.
Remaining apples for sale = $10 - 1 = 9$ kg.
3. Desired Selling Price (SP) for 10% profit:
Desired profit = 10% of CP = $0.10 \times 405 = \text{Rs. } 40.50$.
Desired SP = CP + Profit = $405 + 40.50 = \text{Rs. } 445.50$.
4. Rate per kg for remaining apples:
To achieve the desired SP of Rs. 445.50 by selling 9 kg of apples:
Rate per kg = $\frac{\text{Desired SP}}{\text{Remaining apples}} = \frac{445.50}{9} = \text{Rs. } 49.50 \text{ per kg}$.

Step 4: Final Answer:
The rate at which he should sell the remaining apples per kg is Rs. 49.50.