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

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

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29 Oct 2018, 01:25
00:00

Difficulty:

55% (hard)

Question Stats:

68% (01:45) correct 32% (01:35) wrong based on 34 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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A grocer bought 24Kg of coffee beans at price X. After a while one thi  [#permalink]

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29 Oct 2018, 01:51
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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30 Oct 2018, 01:18
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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Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3334
Location: India
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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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30 Oct 2018, 01:23
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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30 Oct 2018, 02:34

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

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Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
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Re: A grocer bought 24Kg of coffee beans at price X. After a while one thi &nbs [#permalink] 30 Oct 2018, 02:34
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