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A shipment of 1500 heads of cabbage, each of which was approximately

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A shipment of 1500 heads of cabbage, each of which was approximately [#permalink] New post 10 Feb 2011, 22:16
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

82% (02:39) correct 18% (01:43) wrong based on 22 sessions
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit on this shipment?

a) $100
b) $115
c) $125
d) $130
e) $135

[Reveal] Spoiler:
Total number of heads=1500
cost=600

Cost per head=1500/600=2.5
2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help
[Reveal] Spoiler: OA

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Re: A shipment of 1500 heads of cabbage, each of which was approximately [#permalink] New post 11 Feb 2011, 01:36
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Quote:
Total number of heads=1500
cost=600

Cost per head=1500/600=2.5; not correct

1500\quad head = \$600
1 head = \frac{600}{1500}


2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help


I recommend one should use fractions to solve this one rather than converting it into decimals

Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)

25% more of (2/5) -> 125/100 * 2/5 = $(1/2)

He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500

Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225

Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600

Profit = 725-600 = $125

Ans: "C"
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Joined: 10 Nov 2010
Posts: 268
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 78 [0], given: 22

Re: A shipment of 1500 heads of cabbage, each of which was approximately [#permalink] New post 12 Feb 2011, 12:23
fluke wrote:
Quote:
Total number of heads=1500
cost=600

Cost per head=1500/600=2.5; not correct

1500\quad head = \$600
1 head = \frac{600}{1500}


2/3(1500)=1000
cost of 1000 heads=2.5*1.25*1000=3130
cost of rest 500 heads=3(500)=1500

Gross profit =4630-600=4030

But this answer is wrong.I think the method I am using is correct.

Where is the problem?
Pls help


I recommend one should use fractions to solve this one rather than converting it into decimals

Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)

25% more of (2/5) -> 125/100 * 2/5 = $(1/2)

He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500

Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225

Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600

Profit = 725-600 = $125

Ans: "C"

Thanks
I was wrong while calculating cost per head
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Re: A shipment of 1500 heads of cabbage, each of which was approximately [#permalink] New post 13 Feb 2011, 03:29
1.25 * 2/3 * 1500 * 600/1500 - Day 1 Total SP

0.9 * 1.25 * 1/3 * 1500 * 600/1500 - Day 2 total SP


=> Total SP = 600/1500 * 1500 * 1.25 (2/3 + 0.9 * 1/3)

= 600 * 5/4 * (2 + 0.9)/3

= 3000 * 2.9/12 = 725

=> Profit = 725 - 600 = $ 125
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Re: A shipment of 1500 heads of cabbage, each of which was approximately [#permalink] New post 02 Jan 2015, 10:28
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Re: A shipment of 1500 heads of cabbage, each of which was approximately   [#permalink] 02 Jan 2015, 10:28
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