A trader bought 30 articles. He sold 20 of them at a gain of 16% and sold the remainder at a loss of 4%.Find the percentage profit/loss on the articles.
Let CP be the cost price of the 30 articles.
Total cost of the 30 articles is 30*CP.
Income
20 articles @ 16% profit brings in 20*CP*(1 + 0.16) = 20CP(1.16)
10 articles @ 4% loss brings in 10*CP*(1 – 0.04) = 10CP(0.96)
Total income is: 20CP(1.16) + 10CP(0.96)
Overall Profit/Loss
Profit = (Total Income)/(Total Cost)
Profit = (20CP(1.16) + 10CP(0.96))/( 30CP)
Profit = (2/3)*1.16 + (1/3)*0.96
Profit = 0.77333 + 0.32
Profit = 1.09333
Answer: Profit is 9 1/3 % gain