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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?
  • a)
    96
  • b)
    98
  • c)
    86
  • d)
    84
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A wholesaler bought walnuts and peanuts, the price of walnut per kg be...
Let the price of peanuts be Rs. 100x per kg
Then, the price of walnuts = Rs. 300x per kg
Cost price of peanuts for the shopkeeper = Rs. 110x per kg
Cost price of walnuts for the shopkeeper = Rs. 360x per kg
Total cost incurred to the shopkeeper while buying = Rs.(8 * 110x + 16 * 360x) = Rs. 6640x
Since, 5kg walnut and 3kg peanuts are lost in transit, the shopkeeper will be remained with (16-5)+(8-3)=16kgs of nuts
Total selling price that the shopkeeper got = Rs. (166 * 16) = Rs. 2656
Profit = 25%
So, cost price = Rs. 2124.80
Therefore, 6640x = 2124.80
On solving, we get x = 0.32
Therefore, price of walnuts = Rs. (300 * 0.32) = Rs. 96 per kg.
Hence, option A is the correct answer
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Most Upvoted Answer
A wholesaler bought walnuts and peanuts, the price of walnut per kg be...
Let's assume the cost price of peanuts per kg is x.

According to the given information, the cost price of walnuts per kg is thrice that of peanuts, so the cost price of walnuts per kg is 3x.

Profit on peanuts = 10%
Profit on walnuts = 20%

The shopkeeper bought 8 kg of peanuts from the wholesaler and sold them at a profit of 10%. So, the selling price of 8 kg of peanuts = cost price of 8 kg of peanuts + profit on 8 kg of peanuts.
Selling price of 8 kg of peanuts = 8x + 0.10 * 8x = 8x + 0.8x = 8.8x

Similarly, the shopkeeper bought 16 kg of walnuts from the wholesaler and sold them at a profit of 20%. So, the selling price of 16 kg of walnuts = cost price of 16 kg of walnuts + profit on 16 kg of walnuts.
Selling price of 16 kg of walnuts = 16 * 3x + 0.20 * 16 * 3x = 48x + 9.6x = 57.6x

Now, let's consider the loss in transit.
The shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. So, the remaining peanuts = 8 - 3 = 5 kg and the remaining walnuts = 16 - 5 = 11 kg.

The shopkeeper mixed the remaining nuts and sold the mixture at Rs. 166 per kg, making an overall profit of 25%.

Let's assume the cost price of the mixed nuts per kg is y.
According to the given information, the selling price of the mixed nuts per kg is Rs. 166.

So, the cost price of the mixed nuts per kg + profit on the mixed nuts = selling price of the mixed nuts per kg.
y + 0.25y = 166
1.25y = 166
y = 166/1.25 = 132.80

Since the cost price of the mixed nuts per kg is the average of the cost prices of peanuts and walnuts, we can write the following equation:
(5x + 11 * 3x) / 16 = 132.80

Solving this equation, we get:
8x = 16 * 132.80
8x = 2124.80
x = 2124.80/8 = 265.60/8 = 33.20

Therefore, the price, in Rs. per kg, at which the wholesaler bought the walnuts is 3x = 3 * 33.20 = 99.60 ≈ 96 (option A).
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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?a)96b)98c)86d)84Correct answer is option 'A'. Can you explain this answer?
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