CAT 2018 [SLOT 1] Quant Question with Solution 19

Question:
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 pro?t of 10% and 16 kg of walnuts at a pro?t 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 pro?t of 25%. At what price, in Rs. per kg, did the wholesaler buy the walnuts?

  1. 98
  2. 96
  3. 84
  4. 86
Show Answer
Correct Answer: 2
Let the cost price of peanuts for the wholesaler be x per kg.
Cost price of walnuts for the wholesaler is 3x per kg.
The wholesaler sold 8 kg of peanuts at 10% profit and 16 kg of walnuts at 20% profit to a shopkeeper.
Total cost price to the shopkeeper = (8)(x)(1.1) + 16(3x)(1.2) = 66.4x
The shopkeeper lost 5 kg walnuts and 3 kg peanuts.
The shopkeeper sold the mixture of 11 kg walnuts and 5 kg peanuts.
His total selling price=166(16) = 2656
His total cost price $=2656\left(\frac{100}{125}\right)=2124.8$
$66.4 x=2124.8$
$x=32$
Price at which the wholesaler bought walnuts = 3x = 96/- per kg

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