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

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
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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

Video solution from Quant Reasoning starts at 20:24
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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

This sol might help, its faster if we solve this way , might save you some time

Prob:
Total number of heads=1500
Cost Price =$600
Sale Price = 2/3 sold at 25% profit & 1/3 sold at price (10% less than the price each head sold for the day before)

Sol: will calculate these in bulks only (will try not to go down to single level)

2/3 of 1500 ~ 1000 --> sold on day 1
1/3 of 1500 ~ 500 --> sold on day 2

Day 1: Sale price of 2/3 sold at 25% profit = 1000 * 600/1500 * 125/100 = $500

~~now 1000 heads sold at $500, with the same price could have sold remaining 500 heads for = $500/2 = $250*

Day 2:Sale price of 1/3 (=500 heads) sold at 10% less than previous day price, that's 10% less of $250 = $225 (90% of $250)

Total sale price (Day1 + Day2) = $500 + $225 = $725

Profit = SP - CP = $725 - $600 = $125

Ans C

Profit per unit works well with these numbers.

(Profit per item) * (# items) = gross profit

Cost per cabbage is $600 for 1500 heads = 40¢ per head

Sell Price A is 25% above cost: 40¢ * 1.25 = 50¢. Profit per head for price A = 10¢ = .10

Sell Price B is 10% less than Sell Price A: 50¢ *.90 = 45¢. Profit per head for price B = 5¢ = .05

Number of items at price A = 2/3 of 1,500 = 1,000

Number of items at price B = 1/3 of 1,500 = 500

1,000 * .10 = $100
500 * .05 = $25

Gross profit = 100 + 25 = $125

Answer C
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The rest of your calculations are correct.
But its 40 * 1.25 = 50(because its 25% more than the cost)

Please make the necessary change!

Thanks for catching my typo! Edited.
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hello highly intellectally smart people please help a passionate problem solver

here is my solution which is wrong, but i dont understand why its wrong:) why why why

total number of gabbage 1500

original cost per gabbage \(600/1500\) = 0.30 cents

2/3 of gabbage sold at 0.25 % more than it was bought --> 0.30*1.25 = 37.5 (profit of 2/3 of gabbage sold 7,5 * 1000 = 7500 -->7500/100 = 75

rest of gabbage is sold at 10 % less than day before ---> 37.5 * 0.1 = 3.75 ---> 37,5-3,75 = 33.75 so profit 3.75*500 =1875 --> 1875/100 = 18.75

total profit 75+18,75 = 93.75 why

Hi dave13 , you are indeed a passionate problem solver, which is admirable.

It looks to me as if you mostly understand how to solve the problem. You have a couple of arithmetic mistakes.


Try that arithmetic again.


Whoops. 10 % LESS than means
90 percent OF
(1 - .10) = .90
Not one-tenth

X percent less = (1 - Xpercent)
See below for links on GMAT and percents

If you get stuck trying to decide what "10% less than" means, take a simple example.

A cake cost $100
Next day it is on sale for10% LESS than before
Did the cake cost $10? No.

(1.00 - .10) = .90
The cake sold for .90 * $100 = $90

Finally, I don't understand this part

37.5 CENTS (wrong number, but that's not the point) = .375 DOLLARS
Total revenue on 1,000 = (.375 * 1,000) = $375
??? I think? Am I missing something?

Try again? You'll get it.

See mikemcgarry Percents on the GMAT
And more on GMAT percents HERE:
"For example, the multiplier for a 40% increase would be: 1 + 0.40 = 1.4, and the multiplier for a 40% decrease would be 1 – 0.40 = 0.6 . . ."

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Cost per cabbage = $600/1500 = $0.40
1000 cabbages sold for 25% above cost on day 1: profit on day 1 = 1000*0.25*0.40 = 100
500 cabbages sold for 10% less than day before on day 2: profit on day 2 = 500*(0.50*0.90 - 0.40) = 500*(0.05) = 25
Profit = 100 + 25 = 125

Solutions as presented above are too time-consuming.

profit = revenue-cost
100 = 5/4*400-400
25 = 5/4*9/10*200-200

100+25 = 125
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Let X be CP of each head
on 2/3 of shipments they earn 25 % profit on each = 1.25 X
and on 1/3 of shipments they earn 90% (25% of profit ) = .9* 1.25 X = 1.125 X which is 12.5 % above CP

So we have for every 3 cabbage heads 2 sell @ 25% above CP and 1 sells for 12.5 % above CP

So average profit would be = \(\frac{2*25+12.5*1}{3}\) % of 600

this \(\frac{62.5}{{3}% \) of 600

or \(\frac{62.5}{{300} \) * 600

125

Alternatively,

We know that
on 2/3 ( 1000) of shipments they earn 25 % profit on each = 5/4 on each
and
on 1/3 ( 500) of they earn 90% (25% of profit )= 90/100 *5/4= 9/8 on each
we can find the average profit on entire shipment which comes out to be 29/24
I mostly use allegation method for this
\(\frac{\frac{5}{4}-x}{x-\frac{9}{8}}\) =\(\frac{1}{2}\)

X= 29/24

So (29/24)* 600 -600 = Profit

= 125

Hope this helps
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Use weighted Averages

One end of scale:
(5/4) * (9/10) = 9/8
Second end of scale:
5/4 => 10/8

9/8 ----------Avg-----10/8
Ratio: ----2--------1--

9/8 + 2/3*1/8 = 29/24
% increase = 5/24

Profit = (5/24) * 600 = 125

ANSWER: C

VeritasKarishma,

Can you please explain that how did you interpret the highlighted relationship?

Thanks!

dabaobao,

Can you please explain the rational for defining two ends of scale and above highlighted part?

Thanks!

All the cabbages have the same cost price ($600/1500 = $0.40)

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 (i.e. 1/3 of the heads were sold)

This gives us a ratio of 2 : 1 for the number of heads sold on day 1 : day 2 (2 heads were sold on day 1 for every 1 head on day 2)

Since cost of each head is the same, ratio of cost price on day 1 : day 2 is also 2 : 1 (cost price on day 1 is 2*0.4 for every 0.4 on day 2)