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03 Apr 2020, 06:15
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
56% (03:05) correct
44%
(03:25)
wrong
based on 132
sessions
History
Date
Time
Result
Not Attempted Yet
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 $166 per kg, thus making an overall profit of 25%. At what price, in $ per kg, did the wholesaler buy the walnuts?
A. 84
B. 86
C. 88
D. 96
E. 98
A. 84
B. 86
C. 88
D. 96
E. 98
03 Apr 2020, 08:23
Kudos
Bookmarks
Let's say the price of peanuts per kg is p
The price of walnut per kg being thrice that of peanut per kg will be 3p.
8 kg of peanuts would cost him 8p. Now since he sold the 8 kg of peanuts at a 10% profit, he earned 110%(8p) => 11/10 (8p) => 88p/10.
Similarly 16 kg of walnuts would cost him 48p, and since he sold them at a 20% profit, he earned 120% (48p) => 6/5 (48p) => 288p/5
The shopkeeper who bought the products from the wholesaler lost some of the product in transit; therefore he was finally left with 11 kg of walnuts and 5 kg of peanuts. He then mixed the remaining nuts, and this brought the total quantity to 16 kg.
The shopkeeper's per kg price is $166 => Total amount earned by shopkeeper for 16 kg = 16 * 166 => 2656.
Now since the shopkeeper made a profit of 25% on his entire purchase of 8 kg of peanuts and 16 kg of walnuts = 125%(88p/10 + 288p/5)
And this 125%(88p/10 + 288p/5) is equal to 2656
5/4(88p/10 + 288p/5) = 2656
=> p = 32.
Since the price of walnut per kg is 3p.
Therefore, 3*32 = 96.
Answer: D
The price of walnut per kg being thrice that of peanut per kg will be 3p.
8 kg of peanuts would cost him 8p. Now since he sold the 8 kg of peanuts at a 10% profit, he earned 110%(8p) => 11/10 (8p) => 88p/10.
Similarly 16 kg of walnuts would cost him 48p, and since he sold them at a 20% profit, he earned 120% (48p) => 6/5 (48p) => 288p/5
The shopkeeper who bought the products from the wholesaler lost some of the product in transit; therefore he was finally left with 11 kg of walnuts and 5 kg of peanuts. He then mixed the remaining nuts, and this brought the total quantity to 16 kg.
The shopkeeper's per kg price is $166 => Total amount earned by shopkeeper for 16 kg = 16 * 166 => 2656.
Now since the shopkeeper made a profit of 25% on his entire purchase of 8 kg of peanuts and 16 kg of walnuts = 125%(88p/10 + 288p/5)
And this 125%(88p/10 + 288p/5) is equal to 2656
5/4(88p/10 + 288p/5) = 2656
=> p = 32.
Since the price of walnut per kg is 3p.
Therefore, 3*32 = 96.
Answer: D
04 Apr 2020, 02:16
Kudos
Bookmarks
Bunuel
Solution
- • Let us assume that the wholesaler bought the peanuts and the walnuts at a cost price of , \(x\) and \(3x\) ($ per kg) respectively.
• Total cost price for the shopkeeper = Total selling price for the wholesaler \(= \frac{110}{100}*8x + \frac{120}{100}*16*3x = (\frac{44x}{5 }+ \frac{16*6*3x}{5})\) $
• The amount of mixture sold by shopkeeper \(= (16 – 5) + (8 -3) = 11+5 =16\) kg.
- o Thus, selling price for the shopkeeper \(= (16*166)\) $
- o Thus, \(16*166 = \frac{5}{4} * (\frac{44x}{5} + \frac{16*6*3x}{5})\)
\(⟹11x+72x = 16*166\)
\(⟹83x = 16*166\)
\(⟹ x = 16*2 = 32\)
\(⟹ 3x = 32*3 = 96\)
