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During a sale, 50% of the goods are sold at a 49% profit, 32% of the remaining goods are sold at a 45% profit and the still remaining goods are sold at a loss of 15%. If there is an overall profit of x%, then what is the value of x?
27%
26.6%
28.1%
25%
27%
Assume total goods = 100 units. Profit1 = 50 * 49 = 2450. Remaining = 50. 32% of 50 = 16. Profit2 = 16 * 45 = 720. Final rest = 50 - 16 = 34. Loss3 = 34 * -15 = -510. Total Profit = 2450 + 720 - 510 = 2660. Net % = 2660 / 100 = 26.6%. Wait, check options: 27% is given as answer, recalculating: 50% * 49 + 16% * 45 + 34% * -15 = 24.5 + 7.2 - 5.1 = 26.6%. The provided answer key might be approximated or contains a discrepancy; however, 26.6% is the accurate mathematical result.
50% goods at 49% profit, 32% of remaining at 45% profit, and the rest at 15% loss.
x=w1+w2+w3(w1⋅P1)+(w2⋅P2)+(w3⋅P3)
Assume total goods = 100 units. Profit1 = 50 * 49 = 2450. Remaining = 50. 32% of 50 = 16. Profit2 = 16 * 45 = 720. Final rest = 50 - 16 = 34. Loss3 = 34 * -15 = -510. Total Profit = 2450 + 720 - 510 = 2660. Net % = 2660 / 100 = 26.6%. Wait, check options: 27% is given as answer, recalculating: 50% * 49 + 16% * 45 + 34% * -15 = 24.5 + 7.2 - 5.1 = 26.6%. The provided answer key might be approximated or contains a discrepancy; however, 26.6% is the accurate mathematical result.
Students often calculate 32% of the total 100 instead of 32% of the 'remaining' goods (50 units).
Calculate quantities
Assume total goods = 100. Part 1 = 50 units (at 49% profit). Remaining = 50 units. Part 2 = 32% of 50 = 16 units (at 45% profit). Part 3 = 50 - 16 = 34 units (at 15% loss).
Q1=50,Q2=16,Q3=34
Calculate total profit
Sum the profit/loss for each part: (50×49)+(16×45)+(34×−15)=2450+720−510=2660.
Total Profit=2660
Calculate x
The overall profit percentage x is the total profit divided by total units: x=2660/100=26.6.
x=26.6%
B is correct because the weighted average calculation yields an overall profit of 26.6%.
This weighted average method is identical to calculating the combined mean in statistics and mixture/alligation problems.