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Math Expert V
Joined: 02 Sep 2009
Posts: 60646
A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 55% (02:18) correct 45% (02:10) wrong based on 87 sessions

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A grocer bought 24Kg of coffee beans at price X. After a while one third of the stock got spoiled so he sold the rest for 200$per Kilo and made a total profit of twice the cost. What must be price X? A. 66 2/3$.

B. 50 1/3$. C. 44 4/9$.

D. 33 1/3$. E. 24 1/2$.

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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3286
Location: India
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A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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Bunuel wrote:
A grocer bought 24Kg of coffee beans at price X. After a while one third of the stock got spoiled so he sold the rest for 200$per Kilo and made a total profit of twice the cost. What must be price X? A. 66 2/3$.

B. 50 1/3$. C. 44 4/9$.

D. 33 1/3$. E. 24 1/2$.

The grocer bought 24 kg of coffee beans at X and sold 16 kg(as one-third of stock
got spoiled) of the stock for 200$per kilo. The total profit made is twice the cost. Profit = Selling Price - Cost Price So, $$16*200 - 24*x = 2*24x$$ This can be further simplified as $$72x = 16*200$$ -> $$x = \frac{16*200}{72} = \frac{400}{9}$$ Therefore, the price at which the grocer bought the coffee beans is$$$44\frac{4}{9}$$ (Option C)
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3230
Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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pushpitkc wrote:
Bunuel wrote:
A grocer bought 24Kg of coffee beans at price X. After a while one third of the stock got spoiled so he sold the rest for 200$per Kilo and made a total profit of twice the cost. What must be price X? A. 66 2/3$.

B. 50 1/3$. C. 44 4/9$.

D. 33 1/3$. E. 24 1/2$.

The grocer bought 24 kg of coffee beans at X and sold 16 kg(as one-third of stock
got spoiled) of the stock for 200$per kilo. The total profit made is twice the cost. Profit = Selling Price - Cost Price So, $$16*200 - 24*x = 2*24x$$ This can be further simplified as $$72x = 16*200$$ -> $$x = \frac{16*200}{72} = \frac{200}{9}$$ Therefore, the price at which the grocer bought the coffee beans is$$$44\frac{4}{9}$$ (Option C)

There is a small calculation mistake in the end.

16 * 200/72 = 400/9
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Senior PS Moderator V
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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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EgmatQuantExpert wrote:
pushpitkc wrote:
Bunuel wrote:
A grocer bought 24Kg of coffee beans at price X. After a while one third of the stock got spoiled so he sold the rest for 200$per Kilo and made a total profit of twice the cost. What must be price X? A. 66 2/3$.

B. 50 1/3$. C. 44 4/9$.

D. 33 1/3$. E. 24 1/2$.

The grocer bought 24 kg of coffee beans at X and sold 16 kg(as one-third of stock
got spoiled) of the stock for 200$per kilo. The total profit made is twice the cost. Profit = Selling Price - Cost Price So, $$16*200 - 24*x = 2*24x$$ This can be further simplified as $$72x = 16*200$$ -> $$x = \frac{16*200}{72} = \frac{200}{9}$$ Therefore, the price at which the grocer bought the coffee beans is$$$44\frac{4}{9}$$ (Option C)

There is a small calculation mistake in the end.

16 * 200/72 = 400/9

Thanks for notifying - Have made the necessary changes
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3230
Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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Solution

Given:
• Cost price of 24kg of coffee beans = 24 * X
• Sold the rest $$(\frac{2}{3}) * 24kg$$ at a selling price of $200 per kg • Profit = 2 * cost price To find: • The value of X Approach and Working: • Total CP = 24X • Total SP = $$200 * 24 * \frac{2}{3}= 3200$$ • Profit =$3200 – 24X = 2 * 24X
o Implies, $$X = \frac{3200}{72} = \frac{400}{9} = 44\frac{4}{9}$$

Hence, the correct answer is Option C

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Manager  G
Joined: 10 Jun 2019
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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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this is a poorly worded question. The question makes it like the whole 24kg costs X while what the answer really confirms is that 24kg was bought at X per kilo. @Bunuel,this question needs to be reworded
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GMAT 1: 690 Q50 V34 Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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Bunuel wrote:
A grocer bought 24Kg of coffee beans at price X. After a while one third of the stock got spoiled so he sold the rest for 200$per Kilo and made a total profit of twice the cost. What must be price X? A. 66 2/3$.

B. 50 1/3$. C. 44 4/9$.

D. 33 1/3$. E. 24 1/2$.

Given:
1. A grocer bought 24Kg of coffee beans at price X.
2. After a while one third of the stock got spoiled so he sold the rest for 200$per Kilo and made a total profit of twice the cost. Asked; What must be price X? Total initial stock = 24 kg Total cost price =$24X

Stock spoiled = 8 kg
Remaining stock = 16 kg
Total selling price = 16 * 200 = $3200 Total Profit = Total selling price - Total cost price = 3200 - 24X = 48X 72X = 3200 X = 3200/72 = 400/9 =$44 4/9

IMO C
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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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Bunuel wrote:
A grocer bought 24Kg of coffee beans at price X. After a while one third of the stock got spoiled so he sold the rest for 200$per Kilo and made a total profit of twice the cost. What must be price X? A. 66 2/3$.

B. 50 1/3$. C. 44 4/9$.

D. 33 1/3$. E. 24 1/2$.

CP of 24 Kgs = 24x

1/3rd of 24 kg spoilt , so we are left with 2/3rd = 16 kgs and he sells it 200 / kg , so SP = 3200

SP - CP = Profit

So, 3200 - 24x = 48x

Or, 72x = 3200

So, x = 44 4/9 , Answer must be (C)
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Intern  B
Joined: 30 Sep 2018
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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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Bunuel wrote:
A grocer bought 24Kg of coffee beans at price X. After a while one third of the stock got spoiled so he sold the rest for 200$per Kilo and made a total profit of twice the cost. What must be price X? A. 66 2/3$.

B. 50 1/3$. C. 44 4/9$.

D. 33 1/3$. E. 24 1/2$.

Hi Bunuel,
I think its important to mention X per kg here to avoid any confusion Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi   [#permalink] 27 Oct 2019, 03:00
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