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.