This is a beautiful question from CAT 2018 Question paper. It is based on ** Mixtures ** that also combines ** Profit and Loss **. The multiple layers such as wholesaler and buyer with the addition of two quantities make it a little tricky. Try your hands on this question before looking at he solution provided. If you want to practice more of **CAT Previous Year Paper**, visit **2IIM's CAT Question Bank**.

Question 7 :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?

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- 96
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Let the wholesaler bought walnuts and peanuts at Rs 3x and Rs x respectively

He sold 8kgs of Peanuts to the shopkeeper at 10% Profit

Cost price of the Peanuts bought by the shopkeeper = Rs. 1.1x per kg

Similarly, he sold 16 kgs of Walnuts to the shopkeeper at 20% Profit

Cost price of the Walnuts bought by the shopkeeper = 1.2 × 3x = Rs. 3.6x per Kg

He lost 5 kgs of Walnuts and 3 Kgs of Peanuts in transit

Remaining = 16 - 5 = 11 kgs of Walnuts & 8-3 = 5 kgs of Peanuts

He mixes them together and sells them at Rs. 166 per kg, making an overall Profit of 25%

Selling Price = \\frac{5}{4}) × Cost Price

Overall Cost Price = Rs.(3.6 × 16x + 1.1 × 8x)

Overall Selling Price = Rs. 16 × 166

Overall Selling Price = \\frac{5}{4}) × Overall Cost Price

(3.6 × 16x + 1.1 × 8x) × \\frac{5}{4}) = 16 × 166

( ( 57.6 × 8.8) x ) × 5/4 = 16 × 166

x = Rs. 32

Cost price per Kg of Walnuts bought by the Wholesaler = Rs. 3x = 3 × 32 = **>Rs. 96**

The question is **"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?" **

Choice C is the correct answer.

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