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During a sale, 44% of the goods are sold at a profit of 47%. Of the remaining goods, 25% are sold at a profit of 22%, and the rest are sold at a loss of 38%. If the overall profit is x%, what is the value of x?
18.5
18
7.8
12.4
7.8
Assume total goods = 100. Calculate weighted sum: (44 * 47) + (14 * 22) - (42 * 38). Divide by 100 to get the overall percentage directly.
44% sold at 47% profit, 25% of the remaining (which is 14%) sold at 22% profit, and the rest (42%) sold at 38% loss.
x=тИСwiтАЛтИС(wiтАЛ├ЧpiтАЛ)тАЛ
Assume total goods = 100. Calculate weighted sum: (44 * 47) + (14 * 22) - (42 * 38). Divide by 100 to get the overall percentage directly.
Students often calculate 25% of the total goods (25) instead of 25% of the remaining goods (25% of 56 = 14).
Calculate quantity weights
Total goods = 100 units. First portion = 44 units. Remaining = 100 - 44 = 56 units. Second portion = 25% of 56 = 14 units. Third portion = 56 - 14 = 42 units.
W1тАЛ=44,W2тАЛ=14,W3тАЛ=42
Calculate profit/loss values
Weighted sum = (44 * 47) + (14 * 22) + (42 * -38).
(44├Ч47)+(14├Ч22)тИТ(42├Ч38)=2068+308тИТ1596
Final Calculation
Sum = 2376 - 1596 = 780. Overall percentage x = 780 / 100 = 7.8%.
x=7.8
C is correct because the weighted average calculation yields an overall profit of 7.8%.
This weighted average technique is identical to calculating the combined mean in Statistics and the final concentration of mixture problems in Alligation.
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