Wholesaler Walnut and Peanut Purchase Price

CAT 2019 Slot 1 · QA · Medium · Mixtures

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A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold 8 kg of peanuts at a profit of 10% and 16 kg of walnuts at a profit of 20% to a shopkeeper. However, the shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. 166 per kg, thus making an overall profit of 25%. At what price, in Rs. per kg, did the wholesaler buy the walnuts?

  1. A.

    84

  2. B.

    86

  3. C.

    96

  4. D.

    98

Answer

C

Explanation

Let wholesaler's buying price of peanuts = pp, walnuts = 3p3p. Wholesaler sells to shopkeeper: 8 kg peanuts at 10% profit = 8×1.1p=8.8p8 \times 1.1p = 8.8p. 16 kg walnuts at 20% profit = 16×1.2(3p)=57.6p16 \times 1.2(3p) = 57.6p. Shopkeeper's total cost = 8.8p+57.6p=66.4p8.8p + 57.6p = 66.4p.

Shopkeeper remaining quantity = (16−5)+(8−3)=11+5=16(16 - 5) + (8 - 3) = 11 + 5 = 16 kg. Shopkeeper total revenue = 16×166=265616 \times 166 = 2656. Shopkeeper profit = 25% ⇒1.25×66.4p=2656\Rightarrow 1.25 \times 66.4p = 2656. 83p=2656⇒p=3283p = 2656 \Rightarrow p = 32. Wholesaler bought walnuts at 3p=3×32=963p = 3 \times 32 = 96.

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