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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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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

61% (02:23) correct 39% (02:17) wrong based on 64 sessions

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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
1
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 18 Jul 2019, 02:22
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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Re: A grocer bought 24Kg of coffee beans at price X. After a  [#permalink]

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Re: A grocer bought 24Kg of coffee beans at price X. After a   [#permalink] 04 Sep 2019, 02:43
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