A trader marks his goods 40% above CP and allowed a discount of 30% on marked price. Find profit or loss%

To solve this problem, let's follow these steps:

1. **Marking Price (MP):** The trader marks his goods 40% above the Cost Price (CP). So, if the Cost Price is \( CP \), the Marked Price \( MP \) is:
   \[
   MP = CP + 0.4 \times CP = 1.4 \times CP
   \]

2. **Selling Price (SP):** The trader allows a discount of 30% on the Marked Price. Therefore, the Selling Price \( SP \) is:
   \[
   SP = MP - 0.3 \times MP = 0.7 \times MP
   \]
   Substituting the value of \( MP \) from step 1:
   \[
   SP = 0.7 \times 1.4 \times CP = 0.98 \times CP
   \]

3. **Profit or Loss Percentage:** The profit or loss percentage is calculated by comparing the Selling Price with the Cost Price. The formula is:
   \[
   \text{Profit or Loss Percentage} = \frac{SP - CP}{CP} \times 100
   \]
   Substituting the values:
   \[
   \text{Profit or Loss Percentage} = \frac{0.98 \times CP - CP}{CP} \times 100
   \]
   \[
   \text{Profit or Loss Percentage} = \frac{-0.02 \times CP}{CP} \times 100 = -2\%
   \]

Since the percentage is negative, this indicates a **2% loss**.

Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. What would the profit or loss percentage be if the discount was 20% instead?
2. If the goods were marked 50% above CP and sold at a 25% discount, what would be the profit or loss percentage?
3. How much should the discount be for the trader to break even?
4. What would happen if the trader marked the goods 30% above CP and gave a 10% discount?
5. How would the profit or loss change if the CP increased by 10%?

**Tip:** In percentage problems, it's essential to maintain the correct order of operations and carefully substitute values into the formulas.

Learn how to calculate profit or loss percentage when goods are marked 40% above cost price and sold with a 30% discount. Understand the formula for profit or loss percentage and follow a step-by-step solution. Suitable for students in Grades 9-12.

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