A trader buys 500 kg. of cotton for Rs. 9000. 10% of this cotton is spoiled due to rain. At what rate (Rs./kg) should he sell the rest to earn 10% profit?

Options

A. 25
B. 30
C. 22
D. 20

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Cost Price (CP) per kg of cotton
The trader buys 500 kg of cotton for Rs. 9000.

\[ \text{CP per kg} = \frac{\text{Total Cost}}{\text{Total Weight}} = \frac{9000}{500} = 18 \text{ Rs./kg} \]

**Hint:** To find the cost price per kg, divide the total cost by the total weight of the cotton.

### Step 2: Calculate the amount of spoiled cotton
10% of the cotton is spoiled due to rain.

\[ \text{Spoiled Cotton} = 10\% \text{ of } 500 \text{ kg} = \frac{10}{100} \times 500 = 50 \text{ kg} \]

**Hint:** To find the amount spoiled, calculate 10% of the total weight of cotton.

### Step 3: Calculate the remaining cotton
Subtract the spoiled cotton from the total cotton to find out how much is left.

\[ \text{Remaining Cotton} = 500 \text{ kg} - 50 \text{ kg} = 450 \text{ kg} \]

**Hint:** To find the remaining cotton, subtract the spoiled amount from the total amount.

### Step 4: Calculate the Selling Price (SP) for a 10% profit
To earn a 10% profit, the selling price must be 110% of the cost price.

\[ \text{Total Cost Price for 500 kg} = 9000 \text{ Rs.} \]
\[ \text{Required Selling Price} = 110\% \text{ of } 9000 = \frac{110}{100} \times 9000 = 9900 \text{ Rs.} \]

**Hint:** To find the selling price for a profit, multiply the total cost by 110% (or 1.1).

### Step 5: Calculate the Selling Price per kg of the remaining cotton
Now, divide the total selling price by the remaining cotton to find the selling price per kg.

\[ \text{SP per kg} = \frac{\text{Total Selling Price}}{\text{Remaining Cotton}} = \frac{9900}{450} = 22 \text{ Rs./kg} \]

**Hint:** To find the selling price per kg, divide the total selling price by the weight of the remaining cotton.

### Final Answer
The trader should sell the remaining cotton at Rs. 22 per kg to earn a 10% profit.

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