Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
During a sale, 50% of the goods are sold at a profit of 20%. Of the remaining goods, 40% are sold at a profit of 10%, and the rest are sold at a loss of 10%. If the overall profit is x%, what is the value of x?
8%
9%
10%
11%
11%
Assume the total goods equal 100 units with cost price 1 unit each. Calculate total profit units: (50├Ч0.20)+(20├Ч0.10)+(30├ЧтИТ0.10)=10+2тИТ3=9. Wait, recalculating: 50%├Ч20%=10, 20%├Ч10%=2, 30%├Ч(тИТ10%)=тИТ3. Result 10+2тИТ3=9%.
50% goods at 20% profit, 40% of the remaining at 10% profit, and the final rest at 10% loss.
Overall┬аProfit=тИС(wiтАЛ├ЧpiтАЛ)
Assume the total goods equal 100 units with cost price 1 unit each. Calculate total profit units: (50├Ч0.20)+(20├Ч0.10)+(30├ЧтИТ0.10)=10+2тИТ3=9. Wait, recalculating: 50%├Ч20%=10, 20%├Ч10%=2, 30%├Ч(тИТ10%)=тИТ3. Result 10+2тИТ3=9%.
Students often calculate 40% of total goods instead of 40% of the 'remaining' goods, and neglect the negative sign for the loss.
Define Goods Distribution
Assume total goods = 100 units, each costing 1 unit. First part = 50 units. Remaining = 50 units. Second part = 40% of 50 = 20 units. Third part = 50 - 20 = 30 units.
Parts:┬аP1тАЛ=50,P2тАЛ=20,P3тАЛ=30
Calculate Profit/Loss per Section
Calculate the absolute profit or loss contribution of each section: 50├Ч20%=10, 20├Ч10%=2, and 30├Ч(тИТ10%)=тИТ3.
Profit=(50├Ч0.20)+(20├Ч0.10)+(30├ЧтИТ0.10)=10+2тИТ3=9
Determine Overall Percentage
Since total cost is 100 units and total profit is 9 units, the overall percentage is 1009тАЛ├Ч100%=9%.
x=9%
B is correct because the weighted average calculation (0.5├Ч20%)+(0.2├Ч10%)+(0.3├ЧтИТ10%)=10%+2%тИТ3%=9%.
This concept of weighted averages is identical to calculating the combined mean in Statistics and the effective rate of interest in Compound Interest problems.