# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Mixtures Questions | Question 7

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?

1. 84
2. 86
3. 96
4. 98

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##### Method of solving this CAT Question from Mixtures

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?"

##### Hence, the answer is Rs.96

Choice C is the correct answer.

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