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A farmer produced 750 bushels of a certain crop at a cost of $20 per

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A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 28 Jun 2017, 03:41
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A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold (2/3)rd of the bushels for double their production cost and sold the remaining bushels at 25 percent above their production cost, what was the farmer’s gross profit on the sale of the crop?

(A) $11250
(B) $13375
(C) $15000
(D) $18750
(E) $26250

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Re: A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 28 Jun 2017, 04:11
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Couple of different ways to go about this.... here is one:

**Notice that the problem is asking for profit so we have to subtract cost from revenue**

Find the total cost:
750 * 20 = 15000

Break the cost up into 1/3rds of production
15000/3 = 5000

2/3rds of the crops are sold for double their cost
10000*2 - 5000*2 = 10000

1/3 is sold for 25% more than cost
5000*1.25 - 5000 = 1250

10000+1250 = 11250

answer A
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Re: A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 28 Jun 2017, 04:17
2/3 (750) * 40 + (750/3) * 25 = $20,000 + $6,250 = $26,250

Gross Profit = $26,250 - (750*$20) = $26,250 - $15,000 = $11,250. Ans - A.
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A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post Updated on: 28 Jun 2017, 06:55
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Bunuel wrote:
A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold (2/3)rd of the bushels for double their production cost and sold the remaining bushels at 25 percent above their production cost, what was the farmer’s gross profit on the sale of the crop?

(A) $11250
(B) $13375
(C) $15000
(D) $18750
(E) $26250



Short Cut Method

On \(\frac{2}{3}\) of production, Gross profit earned was = 100% of $20 = $20
On \(\frac{1}{3}\) of production, Gross profit earned was = $25% of 20 = $5
Weighted average of Gross Profit/Bushel = \(\frac{2}{3}\) 20 + \(\frac{1}{3}\) 5 = \(\frac{45}{3}\) = 15
Total Gross Profit = 15 x 750 = 11250

Hence Answer A
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Originally posted by elegantm on 28 Jun 2017, 05:39.
Last edited by elegantm on 28 Jun 2017, 06:55, edited 2 times in total.
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A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 28 Jun 2017, 06:25
If the cost of production per bushel is x$
From the question stem we know that
CP : 750x
SP : \(500(2x) + 250(\frac{5x}{4}) = 1000x + (\frac{1250x}{4}) = \frac{5250x}{4}\)

Profit earned(due to sale of bushel) =\(\frac{5250x}{4}- 750x\) = \(\frac{(5250x - 3000x)}{4} = \frac{2250x}{4}\)

Since we are given the cost of producing the bushel = 20$(in question stem, putting x=20$)

Cost : \(2250*\frac{20}{4}\) = 2250*5 = 11250$(Option A)
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A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 28 Jun 2017, 09:14
Bunuel wrote:
A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold (2/3)rd of the bushels for double their production cost and sold the remaining bushels at 25 percent above their production cost, what was the farmer’s gross profit on the sale of the crop?

(A) $11250
(B) $13375
(C) $15000
(D) $18750
(E) $26250


Total cost of production = $ 15000

Quote:
If the farmer sold (2/3)rd of the bushels for double their production cost


Selling price of 2/3 rd of the bushels = 10000*2 => 20000

Quote:
sold the remaining bushels at 25 percent above their production cost


Selling price of remaining is \(\frac{125}{100}*5000\) = 6250

Gross Profit = \(20000 + 6250 - 15000\)

So, Gross Profit is (A) 11250
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Re: A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 29 Jun 2017, 01:48
A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold (2/3)rd of the bushels for double their production cost and sold the remaining bushels at 25 percent above their production cost, what was the farmer’s gross profit on the sale of the crop?

Cost of Producing 750 Bushels \(= 750 * $ 20 = $ 15,000\)

2/3 Bushels \(= 750 * \frac{2}{3} = 500\)

2/3 Bushels sold at double the cost \(= $20 * 2 = $40\)

Profit per Bushels for 2/3 sold at double cost \(= $40 - $20 = $20\)

Total Profit by selling 2/3 Bushels at double cost \(= 500 * 20 = $10,000\) ------------------------(1)

Remaining, or 1/3 of Bushels sold at 5% profit \(= $20 + \frac{5}{100} * $20 = $20 + $ 5 = $25\)

Profit per Bushels for 1/3 sold at 5% profit \(= $25 - $20 = $5\)

Total profit by selling 1/3 Bushels at 5% profit \(= $5 * 250 = $1,250\) ------------------------(1)

From (1) & (2) Total Profit

\($10,000 + $1,250 = $11,250\)

Hence, Answer is A
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Re: A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 30 Jun 2017, 09:21
Bunuel wrote:
A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold (2/3)rd of the bushels for double their production cost and sold the remaining bushels at 25 percent above their production cost, what was the farmer’s gross profit on the sale of the crop?

(A) $11250
(B) $13375
(C) $15000
(D) $18750
(E) $26250


We are given that the farmer sold 2/3 of the bushels for double their production cost; thus, he sold them for:

750(2/3)(40) = (500)(40) = $20,000

He also sold the remaining 1/3 of the bushels at 25 percent above their product cost; thus, he sold them for:

(750)(1/3)(1.25)(20) = (250)(25) = $6,250

His cost is 750(20) = $15,000.

Thus, the profit was:

20,000 + 6,250 - 15,000= $11,250

Answer: A
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Re: A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 12 Feb 2019, 05:04
Bunuel wrote:
A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold (2/3)rd of the bushels for double their production cost and sold the remaining bushels at 25 percent above their production cost, what was the farmer’s gross profit on the sale of the crop?


Initial price = 750 * 20 = 15000

New price = 500 * 40(double of 20) + 250 *25 ( 25 percent above their production cost) = 26250

Profit = 26250 - 15000
$11250
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Re: A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 12 Feb 2019, 05:29
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Bunuel wrote:
A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold (2/3)rd of the bushels for double their production cost and sold the remaining bushels at 25 percent above their production cost, what was the farmer’s gross profit on the sale of the crop?

(A) $11250
(B) $13375
(C) $15000
(D) $18750
(E) $26250


Using weighted average:

100% profit on (2/3)rd of the bushels and 25% profit on (1/3)rd of the bushels.

\(Aavg = \frac{100*(2/3) + 25*(1/3)}{1} = 75\)

Average profit is 75% over the entire crop.
\(Profit = (\frac{75}{100}) * (750*20) = $11250\)

Answer (A)
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Re: A farmer produced 750 bushels of a certain crop at a cost of $20 per  [#permalink]

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New post 12 Feb 2019, 06:02
Bunuel wrote:
A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold (2/3)rd of the bushels for double their production cost and sold the remaining bushels at 25 percent above their production cost, what was the farmer’s gross profit on the sale of the crop?

(A) $11250
(B) $13375
(C) $15000
(D) $18750
(E) $26250


total investment = 750 * 20 ; 15,000
out of 750 ; 2/3 ; 500 were sold at 40 $ = 20,000 and other 250 @ 1.25 * 20 = 25 * 250 = 6250
total earned = 20,000+6250 = 26250
gross profit = 26500-15000; 11250
IMO A
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Re: A farmer produced 750 bushels of a certain crop at a cost of $20 per   [#permalink] 12 Feb 2019, 06:02
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