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A fruit seller bought 2000 quarts of berries at 80 cents per quart. If

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A fruit seller bought 2000 quarts of berries at 80 cents per quart. If  [#permalink]

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New post 18 Feb 2018, 23:03
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Question Stats:

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A fruit seller bought 2000 quarts of berries at 80 cents per quart. If 1/4 of the berries become too ripe for sale, what should be the selling price per quart of the remainder so that the gross profit will be 20 percent of the total cost?

(A) $0.25

(B) $0.80

(C) $1.00

(D) $1.10

(E) $1.28

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Re: A fruit seller bought 2000 quarts of berries at 80 cents per quart. If  [#permalink]

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New post 18 Feb 2018, 23:48
Bunuel wrote:
A fruit seller bought 2000 quarts of berries at 80 cents per quart. If 1/4 of the berries become too ripe for sale, what should be the selling price per quart of the remainder so that the gross profit will be 20 percent of the total cost?

(A) $0.25

(B) $0.80

(C) $1.00

(D) $1.10

(E) $1.28


Instead of explicitly calculating, we'll use the logic of percents and ratios.
This is a Logical approach.

If the seller had sold each unit at the original price they would have made 75% of the original price, a 25% loss.
Since they made a 20% profit, then the ratio selling price:original price must be 120:75 = 24:15 = 8:5
So our number is 8:5 * 80 cents = 640/5 = 128 cents = $1.28

(E) is our answer.
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Re: A fruit seller bought 2000 quarts of berries at 80 cents per quart. If  [#permalink]

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New post 18 Feb 2018, 23:54
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Bunuel wrote:
A fruit seller bought 2000 quarts of berries at 80 cents per quart. If 1/4 of the berries become too ripe for sale, what should be the selling price per quart of the remainder so that the gross profit will be 20 percent of the total cost?

(A) $0.25

(B) $0.80

(C) $1.00

(D) $1.10

(E) $1.28



2000 quarts at .8$ cost = 1600$

1/4 quarts wasted.. remaining can be sold = 2000 x 3/4 = 1500

20% of 1600 = 320 $

total cost = 1600 + 320 = 1920

selling price = total cost / quarts remaining == 1920/1500 = 1.28 $

(E) imo
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Re: A fruit seller bought 2000 quarts of berries at 80 cents per quart. If  [#permalink]

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New post 18 Feb 2018, 23:58
Total cost of 2000 quarts of berries= 2000*0.80= $1600

Gross Profit= $1600*\(\frac{20}{100}\) =3200

Selling Price= $1600 + $320= $1920

Remaining berries to be sold= 2000- 500= 1500

Selling price of remaining berries per quart= \(\frac{$1920}{1500}\)= $1.28

Answer: E.
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Re: A fruit seller bought 2000 quarts of berries at 80 cents per quart. If  [#permalink]

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New post 21 Feb 2018, 14:27
Bunuel wrote:
A fruit seller bought 2000 quarts of berries at 80 cents per quart. If 1/4 of the berries become too ripe for sale, what should be the selling price per quart of the remainder so that the gross profit will be 20 percent of the total cost?

(A) $0.25

(B) $0.80

(C) $1.00

(D) $1.10

(E) $1.28


The cost for the berries was c = 2,000 x 0.8 = 1,600 dollars.

The number of quarts of berries sold is 2,000 x 3/4 = 1,500.

Letting r = total revenue, we will use the formula for gross profit, which is r - c. In order for gross profit to be 20% of cost, we need:

r - c = 0.2c

r = 1.2c

r = 1.2(1600) = 1,920

If we let p = the selling price per quart of berries, our revenue will be::

1,500 x p = 1920

p = 1.28

Answer: E
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A fruit seller bought 2000 quarts of berries at 80 cents per quart. If  [#permalink]

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New post 22 Feb 2018, 11:09
Bunuel wrote:
A fruit seller bought 2000 quarts of berries at 80 cents per quart. If 1/4 of the berries become too ripe for sale, what should be the selling price per quart of the remainder so that the gross profit will be 20 percent of the total cost?

(A) $0.25

(B) $0.80

(C) $1.00

(D) $1.10

(E) $1.28

Profit = TR - TC, AND
TR = TC + Profit
Because we can find both TC and profit pretty easily, find what TR must be and divide by number of quarts sold to get sell price per quart

TC, Profit, TR

TR = TC + Profit
TR = (# quarts sold)*(Price, P, per quart)

Find Total Cost:
2,000 quarts at $0.80 per quart
TC = (2,000 * $0.80) = $1,600

Find Profit: 20 percent of TC
Profit= (.20 * $1,600) = $320

TR = $320 + $1,600 = $1,920

Sell price per quart?
Find sell price from the other TR formula

TR =$1,920= (# qrts sold)*(Price, P, per qrt)

How many quarts sold?
(2,000 - 500) = 1,500 quarts sold

At what sell price per item, P?

TR= (# of items)*(sell price per item,P)

\($1,920 =1,500P\)

\(P =\frac{$1,920}{1,500}=$1.28\)


ANSWER E

Once we have
\($1,920 =1,500P\)
there is no need to calculate exactly.
Answers A, B, and C are too small.
Answer C, e.g., $1.00:
1,500*$1.00 = $1,500. Not close to $1,920
Answer D, mental math eliminates. Split $1.10 into $1 and $0.10
1,500 * $1 = $1,500
1,500 * $0.10 = $150
= $1,650 total
By POE, ANSWER E


*Faster: Profit is 20 percent of the total cost = 20 percent more than total cost= TR:
($1,600 * 1.2) = $1,920 = TR

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Re: A fruit seller bought 2000 quarts of berries at 80 cents per quart. If  [#permalink]

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New post 28 Nov 2018, 09:27
Bunuel wrote:
A fruit seller bought 2000 quarts of berries at 80 cents per quart. If 1/4 of the berries become too ripe for sale, what should be the selling price per quart of the remainder so that the gross profit will be 20 percent of the total cost?

(A) $0.25

(B) $0.80

(C) $1.00

(D) $1.10

(E) $1.28


Total cost of 2000 quarts of berries = 2000 * $0.80 = 1600$
After profit of 20%, total selling price will be 1600*1.2 = 1920 $

Since 1/4th quarts are too ripe , so only 3/4 th quarts = 1500 quaarts is left to be sold.. Let the selling price of 1 quart = x
So, 1500 x = 1920 $
x = 1.28 $

Answer E
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Re: A fruit seller bought 2000 quarts of berries at 80 cents per quart. If   [#permalink] 28 Nov 2018, 09:27
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