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10 Feb 2011, 23:16
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C
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Difficulty:
25%
(medium)
Question Stats:
83% (03:04) correct
17%
(03:31)
wrong
based on 2515
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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
(A) $100
(B) $115
(C) $125
(D) $130
(E) $135
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
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
25 May 2017, 15:57
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Quote:
We are given that a shipment of 1500 heads of cabbage costs 600 dollars, or 600/1500 = $0.40 per cabbage.
We are given that 2/3 x 1500 = 1,000 heads of cabbage sold for 1.25 x $0.40 = $0.50. So, a total of 1,000 x $0.50 = $500 was made on the sale of those heads of cabbage.
The next day, 500 heads of cabbage were sold at a price of 0.9 x $0.50 = $0.45, so a total of 500 x $0.45 = $225 dollars was made on the sale of those heads.
Thus, a total of 500 + 225 = $725 was made.
Thus, profit = 725 - 600 = $125.
Answer: C
13 Feb 2011, 04:29
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This question can be solved using the concept of weighted averages.
If weighted averages is your strength, read the following:
Profit % can be averaged using cost price as weight. Since cost price of each cabbage is the same, the ratio of cost price of cabbages sold the first day and those sold the second day is the same as the ratio of number of heads sold the first day and those sold the second day i.e. 2:1
First day, profit % = 25% i.e. selling price is (5/4)cost price
Second day selling price is 9/10 x 5/4 x cost price = 9/8 cost price. This means a profit % of 12.5%
Using weighted averages, Average profit % = (25 x 2 + 12.5 x 1)/3 = 20.8%
20.8% of $600 = $125
If weighted averages is your strength, read the following:
Profit % can be averaged using cost price as weight. Since cost price of each cabbage is the same, the ratio of cost price of cabbages sold the first day and those sold the second day is the same as the ratio of number of heads sold the first day and those sold the second day i.e. 2:1
First day, profit % = 25% i.e. selling price is (5/4)cost price
Second day selling price is 9/10 x 5/4 x cost price = 9/8 cost price. This means a profit % of 12.5%
Using weighted averages, Average profit % = (25 x 2 + 12.5 x 1)/3 = 20.8%
20.8% of $600 = $125
please help a passionate problem solver 
why 
