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The question is a Math Problem Solving question in Arithmetic from the topic Profit and Loss.

By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What will be the percent profit made by the merchant if he sells the article at 95% of its marked price?

1. 5% profit
2. 1% loss
3. 10% profit
4. 5.5% profit
5. 4.5% profit
   
   

The correct choice is (E) and the correct answer is 4.5% profit.

Let the marked price be S and the cost price of the article be C

When the merchant sells at 80% of marked price he sells at 0.8S

This results in a loss of 12%.

Loss is always computed as a percentage of cost price.

Therefore, the loss incurred by the merchant = 0.12C

Hence, he will be selling the article at C - 0.12C = 0.88C when he sells at 80% of his marked price.

Equating the two sides of the relation, we get 0.8S = 0.88C

Or S =

Or S = 1.1C

Now, if the merchant sells at 95% of the marked price, he will be selling at 95% of 1.1C = 1.045C

Hence, the merchant will make a profit of 4.5%.