Practice Questions
Concept Explanation
When two articles with different cost prices and profit percentages are mixed, the overall profit on the mixture is a weighted average of individual profits based on their cost contributions.
Key Formulas
- SP = CP × (1 + profit%/100)
- Mean profit % on mix = (C1P1 + C2P2) / (C1 + C2) when CP is the weight
- Overall SP of mix = total SP / total quantity
Example
10 kg at 20% profit (CP Rs. 100/kg) and 10 kg at 40% profit (CP Rs. 100/kg). Mean profit = (20 + 40)/2 = 30%.
Common Trap
Profit percentages combine by cost weight, not by simple average, when quantities differ.
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Q1 Easy
10 kg CP Rs. 100/kg at 20% profit and 10 kg at 40% profit. Mean profit % is:
ExplanationEqual CP and qty: mean profit = (20 + 40)/2 = 30%. -
Q2 Medium
5 kg CP Rs. 200 at 10% profit, 15 kg CP Rs. 200 at 30% profit. Mean profit % is:
ExplanationWeighted by qty: (5×10 + 15×30)/20 = 500/20 = 25%. -
Q3 Easy
Article A: CP Rs. 80, 25% profit. SP is:
ExplanationSP = 80 × 1.25 = Rs. 100. -
Q4 Medium
20 items CP Rs. 50 at 20% profit and 30 items CP Rs. 50 at 10% profit. Mean profit % is:
Explanation(20×20 + 30×10)/50 = 700/50 = 14%. -
Q5 Easy
CP Rs. 400, SP Rs. 500. Profit % is:
ExplanationProfit = 100/400 = 25%. -
Q6 Medium
12 kg at 15% profit and 8 kg at 45% profit, equal CP Rs. 100/kg. Mean profit % is:
Explanation(12×15 + 8×45)/20 = (180 + 360)/20 = 27%. -
Q7 Easy
Mix of equal qty: 10% profit and 50% profit articles. Mean profit % is:
ExplanationEqual qty: mean = (10 + 50)/2 = 30%.
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Q8 Hard
6 kg CP Rs. 150 at 20% profit and 4 kg CP Rs. 250 at 10% profit. Total SP is:
ExplanationSP = 6×180 + 4×275 = 1080 + 1100 = Rs. 2180. -
Q9 Easy
CP Rs. 500, sold at 15% profit. SP is:
ExplanationSP = 500 × 1.15 = Rs. 575. -
Q10 Medium
8 articles 10% profit and 12 articles 40% profit, same CP Rs. 50. Mean profit % is:
Explanation(8×10 + 12×40)/20 = 560/20 = 28%. -
Q11 Hard
Two mixes same CP: 20% and 30% profit in ratio 2 : 3. Mean profit % is:
ExplanationMean = (2×20 + 3×30)/5 = 130/5 = 26%. -
Q12 Hard
10 kg at 25% profit and 30 kg at 5% profit, CP Rs. 80/kg each. Total profit is:
ExplanationProfit = 10×20 + 30×4 = 200 + 120 = Rs. 320. -
Q13 Medium
SP of mix from equal qty at 15% and 35% profit (CP Rs. 200 each) is per item:
ExplanationMean profit 25%. SP = 200 × 1.25 = Rs. 250. -
Q14 Hard
Which mix has highest mean profit %?
ExplanationA: 20%. B: 25%. C: (20+40)/3 = 23.3%. D: 20%. B is highest.
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DS1 Easy
What is the mean profit percentage?
Statement I10 kg at 20% profit and 10 kg at 40% profit, same CP.
Statement IIEqual quantities at 20% and 40% profit.
ExplanationEach gives mean profit = 30%. -
DS2 Medium
What is the total selling price?
Statement I6 kg CP Rs. 150 at 20% profit.
Statement II4 kg CP Rs. 250 at 10% profit.
ExplanationNeed both: total SP = 1080 + 1100 = Rs. 2180.
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DS3 Medium
Is mean profit greater than 25%?
Statement I5 kg at 10% profit and 15 kg at 30% profit, same CP.
Statement II8 kg at 15% profit and 8 kg at 45% profit, same CP.
ExplanationI gives 25%. II gives 30%. Each alone answers the question. -
DS4 Easy
What is the cost price per kg?
Statement ISP is Rs. 575 at 15% profit.
Statement IIProfit is Rs. 75 on CP Rs. 500.
ExplanationEach gives CP = Rs. 500/kg.