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Profit and Loss 1 / 3

A shopkeeper sells two types of rice, Variety A and Variety B. He mixes them in a certain ratio and sells the mixture at 44 per kg, making a profit of 10%. The cost price of Variety A is 32 per kg and the cost price of Variety B is 50 per kg. If the shopkeeper used a faulty weight of 900g instead of 1kg while selling the mixture, what is the actual profit percentage he made?

(A) 20%

(B) 22.22%

(C) 25%

(D) 33.33%

Correct Answer: (B)
1. Calculate the Cost Price of the Mixture: The selling price of the mixture is 44 per kg at a 10% profit. Therefore, the Cost Price (CP) of the mixture = $44 / 1.1 = 40$ per kg.
2. Find the Mixing Ratio: Using the alligation rule with Variety A (32) and Variety B (50) to get a mean price of 40: The ratio of A to B is $(50 - 40) : (40 - 32) = 10 : 8 = 5 : 4$.
3. Analyze the Faulty Weight Impact: The shopkeeper sells 900g but charges for 1000g. This means his effective Selling Price (SP) is higher. Effective SP = $44 \times (1000 / 900) = 44 \times (10/9) = 440/9$ per real kg.
4. Calculate Actual Profit Percentage: Actual Profit % = $[(\text{Effective SP} - \text{CP}) / \text{CP}] \times 100 = [(440/9 - 40) / 40] \times 100$.
5. Simplify the Expression: $[(440 - 360) / 9] / 40 \times 100 = (80 / 9) / 40 \times 100 = (2 / 9) \times 100 = 22.22\%$.
Test Prep Tip: In complex Profit and Loss problems involving mixtures and faulty weights, always calculate the true cost price of the mixture first using alligation, then apply the "Error Multiplier" (True Weight / False Weight) to the selling price to find the effective profit.

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