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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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During a sale, 55% of the goods are sold at a 41% profit, 20% of the remaining goods are sold at a 19% profit and the rest are sold at a 21% loss. If there is an overall profit of x%, then what is the value of x?
12%
15%
10.5%
16.7%
12%
Assume total goods = 100 units. Then calculate net profit/loss contribution: (55 × 41) + (9 × 19) + (36 × -21) = 2255 + 171 - 756 = 1670. Divide by 100 to get 16.7%. Wait, checking calculation: 5541=2255, 919=171, 36*(-21)=-756. Sum = 2255+171-756 = 1670. Total/100 = 16.7%. Re-evaluating official key claim.
55% goods at 41% profit, 20% of remaining (i.e., 20% of 45% = 9%) at 19% profit, and the rest (36%) at 21% loss.
x=∑i=1n(wi×pi)
Assume total goods = 100 units. Then calculate net profit/loss contribution: (55 × 41) + (9 × 19) + (36 × -21) = 2255 + 171 - 756 = 1670. Divide by 100 to get 16.7%. Wait, checking calculation: 5541=2255, 919=171, 36*(-21)=-756. Sum = 2255+171-756 = 1670. Total/100 = 16.7%. Re-evaluating official key claim.
Students often calculate '20% of remaining' as 20% of total (wrong) rather than 20% of the remaining 45%.
Define Quantities
Assume total quantity of goods is 100 units. Split them based on the given percentages: Group 1 = 55 units, Remaining = 45 units, Group 2 = 20% of 45 = 9 units, Group 3 = 45 - 9 = 36 units.
Q1=55,Q2=9,Q3=36
Calculate Individual Contributions
Multiply each quantity by its respective profit/loss percentage to find total gain/loss points: G1 = 55 × 41, G2 = 9 × 19, G3 = 36 × -21.
Total=(55×41)+(9×19)+(36×−21)
Sum the Contributions
Calculating the values: 55 × 41 = 2255; 9 × 19 = 171; 36 × -21 = -756. Sum = 2255 + 171 - 756 = 1670.
1670
Calculate Overall Profit Percentage
Divide the total points by 100 units to find the overall percentage x%. Note: 1670 / 100 = 16.7%.
x=1001670=16.7%
D is correct because the calculation based on weighted averages yields 16.7% profit.
This weighted average approach is identical to calculating the 'Mean' in Statistics or 'Mixture and Alligation' problems where multiple components are involved.