Question

17. Raghu purchased articles worth 15000. He had to sell 1/3 of these at a loss of 5%. At what profit per cent should he sell the remaining 2/3 articles, so as to make an overall profit of 8%?​

Answer 1

Given :

• CP of articles Raghu purchase = ₹15000
• He sell (1/3) of articles at loss of 5%

To find :

• Profit % of remaining (2/3) or article to make overall profit of 8%

Formula used :

• Loss = CP - SP
• Profit = SP - CP
• Loss % = (Loss×100) ÷ (CP)
• Profit % = (Profit×100)÷ (CP)

Let :

• SP{1}= selling price for (1/3)rd of articles
• SP{2} = selling price for rest (2/3)rd of articles
• CP{1}= cost price for (1/3)rd of articles
• CP{2} = cost price for rest (2/3)rd of articles

Solution :

• First of all we have to find overall profit

Profit% = (Profit ×100) ÷ CP

=> Overall Profit = (Profit%)×(CP) ÷ 100

=> Overall Profit = (8) × 15000 ÷ 100

=> Overall Profit = 1200

• Now , cost price of (1/3)rd of articles , CP{1} = (1/3) of CP

=> CP{1} = 15000/3 = ₹5000

• We are given that, he sold this at loss of 5%, therefore we have to find loss

=> Loss % = (Loss×100)÷(CP)

=> Loss = (Loss%) × ( CP{1}) ÷ 100

=> Loss = 5 × 5000 ÷ 100

=> Loss = ₹250

• We know that , he made overall profit of ₹1200, and he sold (1/3) article at loss of 5% or (₹250)

Overall Profit = Profit by selling (2/3)rd of articles - Loss by selling (1/3)rd of item

=> Profit by selling (2/3)rd of articles = overall Profit + loss by selling (1/3)rd of articles

=> profit by selling (2/3)rd of articles = ₹1200 + ₹250 = ₹1450

• Cost price for (2/3)rd of articles = (2/3)of total CP

=> CP{2} = (2/3)×15000 = ₹10000

also, Profit % = (Profit × 100) ÷ CP{2}

=> Profit% on rest (2/3)rd article = (1450×100) ÷ 10000

=> Profit% on rest (2/3)rd of articles = 145000 ÷ 10000

=> Profit% on rest (2/3)rd of articles = 14.5

ANSWER :

He must sell rest (2/3)rd of articles at Profit of 14.5% so to make overall Profit of 8%