Ram bought 100 articles for RS 4000.he sold of them at a gain of 5% at what gain percent must be sell the remening articles so as to gain 20% on the whole.

How many were sold at a 5% profit?

To find the gain percentage required to earn a profit of 20% on the whole, we need to break down the problem into steps.

Step 1: Calculate the cost price of each article.
Since Ram bought 100 articles for Rs 4000, the cost price of each article is Rs 4000/100 = Rs 40.

Step 2: Calculate the selling price of the first batch of articles.
Ram sold off some articles at a gain of 5%. This means the selling price of each article in the first batch is 105% of its cost price.
Selling price of each article in the first batch = Rs 40 + (5% of Rs 40)
Selling price of each article in the first batch = Rs 40 + (5/100) * Rs 40
Selling price of each article in the first batch = Rs 40 + Rs 2
Selling price of each article in the first batch = Rs 42

Step 3: Calculate the total selling price of the first batch.
Since Ram sold off some of the articles, the total selling price of the first batch can be calculated using:
Total selling price of the first batch = Selling price of each article in the first batch * Number of articles sold in the first batch
Total selling price of the first batch = Rs 42 * (Number of articles sold in the first batch)

Step 4: Calculate the remaining articles.
Since Ram bought 100 articles and sold off some articles, the remaining number of articles can be calculated using:
Remaining articles = Total articles bought - Number of articles sold in the first batch
Remaining articles = 100 - (Number of articles sold in the first batch)

Step 5: Calculate the total selling price of the remaining articles to gain 20% on the whole.
Ram wants to gain 20% on the whole, which means the total selling price of all the articles (first batch + remaining) should be 120% of their cost price.

Total selling price of all the articles = 120% of the total cost price of all the articles
Total selling price of all the articles = (120/100) * (Total cost price of all the articles)
Total selling price of all the articles = (120/100) * (100 * cost price of each article)
Total selling price of all the articles = 1.2 * (100 * cost price of each article)
Total selling price of all the articles = 1.2 * (100 * Rs 40)
Total selling price of all the articles = 1.2 * Rs 4000
Total selling price of all the articles = Rs 4800

Step 6: Calculate the total selling price of the remaining articles.
The total selling price of the remaining articles can be calculated using:
Total selling price of the remaining articles = Total selling price of all the articles - Total selling price of the first batch

Step 7: Calculate the selling price per article for the remaining articles.
The selling price per article for the remaining articles can be calculated using:
Selling price per article for the remaining articles = Total selling price of the remaining articles / Remaining articles

Step 8: Calculate the gain percentage for the remaining articles.
The gain percentage for the remaining articles can be calculated using:
Gain percentage = (Selling price per article for the remaining articles - Cost price per article) / Cost price per article * 100

By following these steps, we can find the gain percentage required for selling the remaining articles to gain 20% on the whole.