A merchant uses a weight of 125 gram instead of 100 gram while buying an article. He used 80 gram instead of 100 gram while selling. He marked up the price by 20% and then offers 20% discount. Find the overall profit or loss percentage.

Buying the Article:

– The merchant buys using a 125 gram weight instead of 100 grams. This means he gets 25% more of the article for the same price. So, the cost price per 100 grams is effectively \(\frac{100}{125} = 0.8\) times the original cost price.

Selling the Article:

– The merchant sells using an 80 gram weight instead of 100 grams. This means he gives 20% less of the article for the same price. So, the selling price per 100 grams is effectively \(\frac{100}{80} = 1.25\) times the original selling price.

Marking Up and Discount:

– The merchant marks up the price by 20% and then offers a 20% discount. The overall effect is calculated as follows:

\[ \text{Overall Factor} = \frac{125}{100} \times \frac{100}{80} \times \frac{120}{100} \times \frac{80}{100} = \frac{3}{2} \]

– This means the selling price is \(\frac{3}{2}\) times the cost price.

Overall Profit Percentage:

– Since the selling price is \(\frac{3}{2}\) times the cost price, the profit is \(\frac{1}{2}\) times the cost price.

– Therefore, the profit percentage is:

\[ \text{Profit Percentage} = \frac{1}{2} \times 100 = 50\% \]

Conclusion

The overall profit percentage is 50%.