Mixture and Alligation: Profit-based Mixtures

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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.

Q1 Easy

A dishonest dealer uses a false weight of 900 g for 1 kg and claims to sell at cost price. His gain percent is:
Q2 Easy

A mixture of 40 kg costs Rs. 2400 and is sold at Rs. 72/kg. Profit percent on the mixture is:
Q3 Easy

Equal quantities of two articles (same CP) are sold at 10% profit and 30% profit. Overall profit percent is:
Q4 Medium

A dishonest dealer professes to sell his goods at cost price, but uses a weight of 960 grams for a kg weight. Find his gain percent.
Q5 Medium

A merchant mixes two varieties of rice costing Rs. 20 and Rs. 30 per kg and sells the mixture at Rs. 27/kg making 8% profit. The ratio of mixing (cheaper : dearer) is:
Q6 Medium

Water is mixed with milk to gain 20% by selling the mixture at cost price. The ratio of milk to water is:
Q7 Medium

A shopkeeper mixes two oils costing Rs. 40/L and Rs. 70/L and sells the mixture at Rs. 60/L making 20% profit. Ratio cheaper : dearer is:

Q8 Medium

A dealer buys wheat at Rs. 30/kg and Rs. 50/kg, mixes them, and sells at Rs. 44/kg for 10% profit. The mixing ratio (cheaper : dearer) is:
Q9 Medium

Milk costing Rs. 40/L is mixed with water and sold at Rs. 40/L for 25% profit. Milk : water is:
Q10 Hard

By mixing two brands of tea A and B costing Rs. 40 and Rs. 50, and selling the mixture at Rs. 46/kg with 15% profit, find the ratio A : B.
Q11 Hard

CP of a mixture is Rs. 60/kg and it is sold at Rs. 72/kg gaining 20%. If pure costs Rs. 80/kg, the quantity of the cheaper variety (Rs. 40/kg) in 100 kg of mixture is:
Q12 Hard

Two types of sugar at Rs. 35/kg and Rs. 55/kg are mixed and sold at Rs. 48/kg for 20% profit. Ratio cheaper : dearer is:
Q13 Hard

A vendor mixes 3 kg of rice at Rs. 24/kg with 5 kg at Rs. 36/kg and sells the mixture at 25% profit. Selling price per kg is:
Q14 Hard

A false weight of 800 g is used for 1 kg while selling at 10% profit on CP. Effective gain percent is:

DS1 Easy

A placement drill asks for gain percent with a false weight. What is the gain percent?

Statement I
The dealer uses 960 g for a 1 kg weight and sells at cost price.

Statement II
He professes to sell at CP but gives only 960 g instead of 1000 g.
DS2 Medium

In a campus mock on profit mixtures, find the mixing ratio of two rices. What is the ratio cheaper : dearer?

Statement I
The two varieties cost Rs. 20/kg and Rs. 30/kg and the mixture is sold at Rs. 27/kg with 8% profit.

Statement II
Only the selling price Rs. 27/kg is known, not the profit percent or the two costs.

DS3 Medium

During an aptitude test, find how much cheaper variety is in 100 kg. What is that quantity?

Statement I
Cheaper costs Rs. 40/kg and dearer Rs. 80/kg; mean CP of mixture is Rs. 60/kg.

Statement II
The mixture is sold at Rs. 72/kg at 20% profit (so mean CP = Rs. 60/kg) with the same two costs.
DS4 Hard

A company screening asks for milk : water when sold at CP for a stated gain. What is the ratio?

Statement I
Gain is 20% and the mixture is sold at the cost price of pure milk.

Statement II
Only the cost of milk per litre is given, not the gain percent.