CAT 2018 Slot 1 — QA Question 8
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
- A
86
- B
84
- C
98
96
Wholesaler:
Assume that the wholesaler bought peanut at Rs. X per kg.
∴ Cost price of walnuts = Rs. 3X per kg
The wholesaler sold peanuts at Rs. 1.1X per kg and walnuts at Rs. 3.6X per kg.
Total cost of 8 kg peanuts and 16 kg walnuts for the shopkeeper = 8 × 1.1X + 16 × 3.6X = 66.4X
∴ Total cost price for Shopkeeper = 66.4X
Shopkeeper:
Shopkeeper's overall profit was 25%
∴ Shopkeeper's revenue = 66.4X × 1.25
He sold (8 – 3 =) 5 kg peanuts and (16 – 5 =) 11 kg walnuts after mixing at Rs. 166 per kg
⇒ 66.4X × 1.25 = 16 × 166
⇒ X = 32
Cost price of walnuts for the wholesaler = 3 × 32 = Rs. 96
Hence, option (d).