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Find the value of X?

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by kishokbabu » Tue Dec 13, 2011 11:07 am
A grocer bought 24 kg of coffee beans at price X per kg. One third of the purchased stock got spoiled, and the grocer sold the remaining coffee beans for $200 per kg. If the grocer made an overall profit that equaled twice the cost price of the purchased stock, what was the original purchased price per kg of coffee beans, X?

A) $66 2/3
B) $50 1/3
C) $44 4/9
D) $33 1/3
E) $24 1/2
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by rijul007 » Tue Dec 13, 2011 11:27 am
kishokbabu wrote:A grocer bought 24 kg of coffee beans at price X per kg. One third of the purchased stock got spoiled, and the grocer sold the remaining coffee beans for $200 per kg. If the grocer made an overall profit that equaled twice the cost price of the purchased stock, what was the original purchased price per kg of coffee beans, X?

A) $66 2/3
B) $50 1/3
C) $44 4/9
D) $33 1/3
E) $24 1/2
Total CP = 24X

Amount of coffee beans lft fr sale = 16kg
SP = $3200

Profit (P) = 2*CP
2*24X = 3200-24X
3*24X = 3200
3X = 400/3
X = 400/9 = 44 4/9

Option C
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by Mdewan » Tue Dec 13, 2011 1:46 pm
Option c
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by GMATGuruNY » Tue Dec 13, 2011 2:05 pm
kishokbabu wrote:A grocer bought 24 kg of coffee beans at price X per kg. One third of the purchased stock got spoiled, and the grocer sold the remaining coffee beans for $200 per kg. If the grocer made an overall profit that equaled twice the cost price of the purchased stock, what was the original purchased price per kg of coffee beans, X?

A) $66 2/3
B) $50 1/3
C) $44 4/9
D) $33 1/3
E) $24 1/2
We can plug in the answers, which represent the cost price per kilogram.
The amount purchased is irrelevant. All that matters is that the profit per kilogram is twice the cost price per kilogram.

Answer choice C: 44 4/9 ≈ 45.
Cost price for 3k = 3*45 = 135.
Selling price for the remaining 2k = 2*200 = 400.
Profit = 400-135 = 265.
Profit/cost = 265/135 ≈ 2.
Success!

The correct answer is C.
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by ranvijay87 » Thu Dec 15, 2011 12:13 am
profit = 2 x Cost Price

-> 2 x 24 = 3200 ?

why is it 2 x 24 = 3200 - 24X?

Please help.
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by rijul007 » Thu Dec 15, 2011 12:35 am
ranvijay87 wrote:profit = 2 x Cost Price

-> 2 x 24 = 3200 ?

why is it 2 x 24 = 3200 - 24X?

Please help.
We jst substituted the values in the equation
Profit = Selling Price - Cost Price
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