An article was purchased for Rs.78.350,Its price was marked up by 30%,It was sold at a discount of 20% on the marked up price.what was the profit percent on the cost price?

In such problems where the marking and discount is for the same article, then we can ignore the cost also. Let the cost price be Rs.100. marked up 30% so marked price Rs.130. After 20% discount - 130 * 80/100 = Rs.104. Profit is 4%

The markup price of the article is 130%*78.350 = Rs. 101.855
The discount given is 20% = 20%*101.855 = Rs. 20.371
Hence, selling price is Rs. 81.484
So, profit is Rs 3.134
So, profit percentage is 4%

Note that in questions like this, the actual cost price is irrelevant. Because, profit percentage is asked, we can ignore the cost price and assume it to be 100 to ease the calculations.
So, mark up price will be Rs. 130
Discount is 20% of 130 = Rs. 26
Sales price is therefore 130-26=Rs. 104 and hence the profit percentage is 4%