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A grocer bought 24Kg of coffee beans at price X. After a while one thi

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

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New post 29 Oct 2018, 02:25
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Question Stats:

54% (02:20) correct 46% (02:10) wrong based on 85 sessions

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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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New post 18 Jul 2019, 02:22
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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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A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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New post 29 Oct 2018, 02:51
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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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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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New post 30 Oct 2018, 02:18
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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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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New post 30 Oct 2018, 02:23
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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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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New post 30 Oct 2018, 03:34

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

Answer: 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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New post 27 Oct 2019, 00:51
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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New post 27 Oct 2019, 01:27
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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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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New post 27 Oct 2019, 03:00
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
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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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