If the selling price of the article is reduced by 40% and the cost price remains the same, the profit reduces by 50% . Find the original profit % of the article 

Let's define the variables first to solve the problem:

- Let $ CP $ be the cost price of the article.
- Let $ SP $ be the original selling price of the article.
- Let $ P $ be the original profit amount.
- Let $ x $ be the original profit percentage.

Given:
1. The selling price is reduced by 40%, so the new selling price becomes $ 0.6 \times SP $.
2. The profit reduces by 50%, so the new profit is $ 0.5 \times P $.

### Step-by-step Solution:

1. **Express Original Profit:**

   The original profit $ P $ can be expressed as:
   \[
   P = SP - CP
   \]

2. **Express Original Profit Percentage:**

   The original profit percentage $ x $ is given by:
   \[
   x = \left( \frac{P}{CP} \right) \times 100
   \]

3. **New Selling Price and New Profit:**

   The new selling price after a 40% reduction is:
   \[
   \text{New } SP = 0.6 \times SP
   \]

   The new profit, which is 50% of the original profit, is:
   \[
   \text{New } P = 0.5 \times P
   \]

4. **Express the New Profit in Terms of the Cost Price:**

   The new profit can also be written as:
   \[
   \text{New } P = \text{New } SP - CP
   \]

   Substituting the values:
   \[
   0.5 \times P = (0.6 \times SP) - CP
   \]

5. **Substitute the Expression for $ P $:**

   Since $ P = SP - CP $, we substitute this into the equation:
   \[
   0.5 \times (SP - CP) = (0.6 \times SP) - CP
   \]

6. **Solve for $ SP $ in Terms of $ CP $:**

   Expand and rearrange the equation:
   \[
   0.5SP - 0.5CP = 0.6SP - CP
   \]

   Combine like terms:
   \[
   0.5SP - 0.6SP = -CP + 0.5CP
   \]

   Simplify further:
   \[
   -0.1SP = -0.5CP
   \]

   Solving for $ SP $:
   \[
   SP = \frac{0.5CP}{0.1} = 5CP
   \]

   So, the original selling price is 5 times the cost price.

7. **Find the Original Profit Percentage:**

   The original profit $ P $ is:
   \[
   P = SP - CP = 5CP - CP = 4CP
   \]

   The original profit percentage $ x $ is:
   \[
   x = \left( \frac{P}{CP} \right) \times 100 = \left( \frac{4CP}{CP} \right) \times 100 = 400\%
   \]

### Conclusion:

The original profit percentage of the article is **400%**.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How would the profit percentage change if the selling price was reduced by 30% instead?
2. What would be the new selling price if the original cost price was \$100?
3. How is the profit margin related to cost and selling prices?
4. Can you derive a formula for the profit percentage change given any reduction in selling price?
5. How would you compute the break-even point for an article given cost and selling prices?

**Tip:** Understanding how profit percentages are affected by changes in selling price can help in making more informed pricing strategies.

If the selling price of the article is reduced by 40% and the cost price remains the same, the profit reduces by 50%. Find the original profit % of the article.

Learn how to calculate the original profit percentage of an article when the selling price is reduced by 40% and the profit reduces by 50%. This step-by-step solution covers key concepts in profit and loss, algebra, and percentage change. Suitable for Grades 10-12.

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