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During a sale, 60% of the goods are sold at a profit of 21%. Of the remaining goods, 40% are sold at a profit of 46%, and the rest are sold at a loss of 29%. If the overall profit is x%, then what is the value of x?
9.5
13
3
3.5
13
Assume total goods = 100. Calculate individual contributions: (60├Ч21)+(16├Ч46)+(24├ЧтИТ29) and divide the final result by 100.
Total goods = 100 units. 60% sold at 21% profit, 40% of remaining (40% of 40 = 16) sold at 46% profit, and the rest (100 - 60 - 16 = 24) sold at 29% loss.
x=тИСWeightiтАЛтИС(WeightiтАЛ├ЧProfitiтАЛ)тАЛ
Assume total goods = 100. Calculate individual contributions: (60├Ч21)+(16├Ч46)+(24├ЧтИТ29) and divide the final result by 100.
Students often fail to calculate the 'remaining' part correctly; 40% of the remaining goods refers to 40% of (100 - 60) = 16 units, not 40% of 100.
Allocate quantities
Assuming total goods = 100 units. Group 1 = 60 units, Group 2 = 40% of (100 - 60) = 16 units, Group 3 = 100 - 60 - 16 = 24 units.
Q1тАЛ=60,Q2тАЛ=16,Q3тАЛ=24
Calculate total profit/loss
Sum the product of each quantity and its corresponding profit/loss percentage: (60├Ч21)+(16├Ч46)+(24├ЧтИТ29).
1260+736тИТ696=1300
Determine overall profit percentage
The overall profit percentage x is the total gain divided by the total number of units.
x=1001300тАЛ=13
B is correct because the weighted average of the profits and losses yields an overall gain of 13%.
This weighted average approach is identical to the method used in Mixture and Allegation problems, where you balance individual concentrations to find the final mixture percentage.
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