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CAT 2018 Slot 1 — QA Question 8

Profit & LossEasy

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? 

Answer & solution

Correct answer: 96

  • A

    86

  • B

    84

  • C

    98

  • 96

Solution

Easy

Let the wholesaler's peanut cost be XX/kg, so walnut cost is 3X3X/kg. He sells 88 kg peanuts at +10%+10\% and 1616 kg walnuts at +20%+20\% to the shopkeeper — that sale value is the shopkeeper's cost. The shopkeeper loses some nuts in transit but still makes 25%25\% profit selling the rest at Rs. 166166/kg. Equate the shopkeeper's revenue to 1.25×1.25\times his cost.

1

Shopkeeper's cost (= wholesaler's selling price). Peanuts sold at 1.1X1.1X, walnuts at 3X×1.2=3.6X3X\times1.2 = 3.6X.

cost=8(1.1X)+16(3.6X)⇒ cost=8.8X+57.6X=66.4X\begin{aligned} &\text{cost} = 8(1.1X) + 16(3.6X)\\ &\Rightarrow\ \text{cost} = 8.8X + 57.6X = 66.4X \end{aligned}
2

Shopkeeper's revenue. After losing 33 kg peanuts and 55 kg walnuts, he has 5+11=165 + 11 = 16 kg, sold at Rs. 166166/kg.

revenue=16×166=2656⇒ revenue=1.25×cost(25% profit)\begin{aligned} &\text{revenue} = 16 \times 166 = 2656\\ &\Rightarrow\ \text{revenue} = 1.25 \times \text{cost} \quad\text{(}25\%\text{ profit)} \end{aligned}
3

Solve for XX. Set revenue =1.25×66.4X= 1.25\times 66.4X.

1.25×66.4X=2656⇒ 83X=2656⇒ X=32\begin{aligned} &1.25 \times 66.4X = 2656\\ &\Rightarrow\ 83X = 2656\\ &\Rightarrow\ X = 32 \end{aligned}
4

Wholesaler's walnut cost. It is 3X3X.

3X=3×32=96\begin{aligned} &3X = 3 \times 32 = 96 \end{aligned}
Rs. 96 per kg  ⇒  option (d)\boxed{\text{Rs. } 96 \text{ per kg} \;\Rightarrow\; \text{option (d)}}

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CAT 2018 Slot 1 QA Q8: A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He the — Solution | TheCATExam