There are 5 packers A, B, C, D, and E in a company. The five

the answer is B
A B C D E
66 54 46 32 28
20 24 30 40 48

A: (100-66)*60*8/20=816
B (100-54)*8*60/24=960
did thesame with C D and E and got 864 and 816 and 720

So if a packer is given from $100, then we have to see for whom the margin of (profit - payout) is greatest

A -> (8 * 60)/20 * (100-66) = (8 * 60)/20 * 34

B -> (8 * 60)/24 * (100-52) = (8 * 60)/24 * 48

C -> (8 * 60)/30 * (100-46) = (8 * 60)/30 * (54)

D -> (8 * 60)/40 * (100-32) = (8 * 60)/40 * (78)

E -> (8 * 60)/48 * (100-28) = (8 * 60)/48 * (72)


Clearly B has max value, so answer - B
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One way is to calculate hourly profit of each worker and compare.

Profit per item for each worker is 100 - cost per item of each worker.

Similarly we know the number of items per hour for each worker as the rate is given.

Hourly profits for each is as below:

A = 34*3 = 102
B = 48*2.5 = 120
C= 54*2 = 108
D=68*1.5 = 102
E=72*1.25 = 90

So, answer is B

A 24(100-66)

B 20(100-52) B gives max

B is the answer..

but isnt there any other easy way?

excuse me, i thought profit=selling price -cost price...
however, you guys all say that profit 100 here is selling price and i really dont understand
can you guy please explain more details

The problem has a lots of information but you can handle it in this simple way.
So

A ---> 66$ each pack work for 8 hours so 480 minutes and each pack require 20 minutes ------> so 480/20 = 24 packs total. Now the profit is 100* 24 packs = 2400 minus the costs that are 66$ * 24 packs = 1584 ----> NET PROFIT 816 $

B ----> the same reasoning lead you to NET PROFIT of 960

At this poit if you look at C D and E lead you to a NET PROFIT less than A or B (if you calculate as above you have less values).

B is the answer. Simple.

PS: kudos if you want
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Hi,

Data is represented in the tabular format:

Answer (B)

Regards,

B it is. This took me more than 5 mins. A guess would have been a more efficient approach...

i would like to know the source of this question.

For me is too time consuming and convoluted for a real gmat question.
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Actually, the question is fair and could be a GMAT question. It takes less than 2 minutes to figure out but I would expect the values to be better in actual GMAT. Let me explain.

Ratio of time taken by the 5 packers is 20:24:30:40:48 = 10:12:15:20:24
Ratio of their speeds must be 1/10:1/12:1/15:1/20:1/24 = 12:10:8:6:5 (by multiplying by LCM = 120)

Obviously, there are packers who work faster than others so they will charge more. The rates would be fair if they charge in the ratio of their speeds i.e. in the ratio 12:10:8:6:5.

But they charge in the ratio 66:52:46:32:28 = 33:26:23:16:14 (this is where I say the numbers could have been better e.g. this ratio could have been 36:28:24:18:15 and the answer would have been a clear B)
Anyway, we work with the numbers we have.

Ratio of their speeds is 12:10:8:6:5 = 36:30:24:18:15 (multiplying by 3 to make it close to the ratio of their charges)

Their speeds ratio is 36:30:24:18:15
Their charges ratio is 33:26:23:16:14
A charges 3/36 = 1/12 less than what he could.
B charges 4/30 = 1/7.5 less than what he could.
C charges 1/24 less than what he could.
D charges 2/18 = 1/9 less than what he could.
E charges 1/15 less than what he could.

Since B gives the maximum discount to the company, he adds most to the company's profit.

I agree with you but form the question is still cumbersome.

By the way, awesome explanation as usual from you
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Packer A: $66 and 20 minutes.

In 8 hours ( 480 minutes) = \(\frac{480 }{ 20}\) = 24 items pack.
Company gets : 24 * 100 = $2,400
Packer A: 24*66 = $1,584
The company left with: $816


Packer B: $52 and 24 minutes.

In 8 hours ( 480 minutes) = \(\frac{480 }{ 24}\) = 20 items pack.
Company gets : 20 * 100 = $2,000
Packer B: 20*52 = $1,040
The company left with $960


Packer C: $46 and 30 minutes.

In 8 hours ( 480 minutes) = \(\frac{480 }{ 30 }\)= 16 items pack.
Company gets : 16 * 100 = $1,600
Packer C: 16*46 = $736
The company left with: $864


Packer D: $32 and 40 minutes.

In 8 hours ( 480 minutes) = \(\frac{480 }{ 40 }\) = 12 items pack.
Company gets : 12 * 100 = $1,200
Packer D: 12*32 = $384
The company left with: $816


Packer E: $28 and 48 minutes.

In 8 hours ( 480 minutes) = \(\frac{480 }{ 48 }\) = 10 items pack.
Company gets : 10 * 100 = $1,000
Packer D: 10*28 = $280
The company left with: $720


Packer B will contributes to the highest net profit.

Answer B

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