The cost price of an article is Rs. $X$. It is marked up by 40% above the cost price, and a discount of 20% is given on the marked price. If the cost price is reduced by Rs. 100 and the selling price increases by Rs. 80, the profit earned on the article becomes 60%. What is the original selling price of the article (in Rs.)?

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**Solution:**

1. Let the cost price be Rs. $X$.

2. The marked price is 40% above the cost price, so:
   $$	ext{Marked Price} = X + 0.40X = 1.4X$$

3. The selling price after a 20% discount on the marked price is:
   $$	ext{Selling Price} = 1.4X 	imes (1 - 0.20) = 1.4X 	imes 0.8 = 1.12X$$

4. According to the problem, the new cost price is reduced by Rs. 100:
   $$	ext{New Cost Price} = X - 100$$

5. The new selling price is Rs. 80 more than the original selling price:
   $$	ext{New Selling Price} = 1.12X + 80$$

6. The profit on the article with the new cost and selling prices is 60%, so:
   $$	ext{Profit} = 60\% \implies 	ext{New Selling Price} = 	ext{New Cost Price} + 0.60 	imes 	ext{New Cost Price} = 1.6 	imes (X - 100)$$

7. Equate the new selling price expressions:
   $$1.12X + 80 = 1.6 (X - 100)$$

8. Expand and simplify:
   $$1.12X + 80 = 1.6X - 160$$

$$80 + 160 = 1.6X - 1.12X$$

$$240 = 0.48X$$

$$X = \frac{240}{0.48} = 500$$

9. The original selling price is:
   $$1.12X = 1.12 	imes 500 = 560$$

**Answer:** Rs. 560

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