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

Question

There are 5 packers A, B, C, D, and E in a company. The five packers A, B, C, D and E charge $66, $52, $46, $32, and $28, respectively, to pack each item. The time taken by the packers to pack one item is 20 minutes, 24 minutes, 30 minutes, 40 minutes and 48 minutes, respectively. All the items are sold at the end of the day. Each item earns a profit of 100 dollars, and the packers are paid from this profit. If each packer works 8 hours a day, which packer contributes the most to the net profit of the company?

A. Packer A
B. Packer B
C. Packer C
D. Packer D
E. Packer E

A. Packer A
B. Packer B
C. Packer C
D. Packer D
E. Packer E

Ans: "B"

Sol:
Each item earns a profit of  100  dollars for the company. If a packer charges x dollars for each item, the profit that the company would effectively get on each item packed would be  100 – x 
Each worker works for  8 hours= 480 minutes . Hence, if a worker takes " t " minutes to pack an item, then he would pack  "480/t"  items each day. So, the net profit on the  \frac{480}{t}  items is  \frac{480}{t}(100-x) . The expression  \frac{480}{t}(100-x)  is a maximum when  \frac{1}{t}(100-x)  is maximum.

We just need to check for what value of "x" and "t", this expression    \frac{100-x}{t}    will be maximum.

A: Packer A; t=20 minutes, x=$66 :     \frac{100-x}{t}=\frac{100-66}{20}=\frac{34}{20}=\frac{17}{10}

B: Packer B; t=24 minutes, x=$52 :    \frac{100-x}{t}=\frac{100-52}{24}=\frac{48}{24}=2

C: Packer C; t=30 minutes, x=$46 :    \frac{100-x}{t}=\frac{100-46}{30}=\frac{54}{30}=\frac{9}{5}

D: Packer D; t=40 minutes, x=$32 :    \frac{100-x}{t}=\frac{100-32}{40}=\frac{68}{40}=\frac{17}{10}

E: Packer E; t=48 minutes, x=$28 :     \frac{100-x}{t}=\frac{100-28}{48}=\frac{72}{48}=\frac{3}{2}

B is maximum at 2 and is the answer.

diebeatsthegmat · Answer

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

subhashghosh · Answer

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

beyondgmatscore · Answer

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

amit2k9 · Answer

A 24(100-66)

B 20(100-52) B gives max

anilwanted · Answer

B is the answer..

but isnt there any other easy way?

diebeatsthegmat · Answer

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

Carcass · Answer

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

cyberjadugar · Answer

Hi,

Data is represented in the tabular format:

Answer (B)

Regards,

OldFritz · Answer

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

Carcass · Answer

i would like to know the source of this question.

For me is too time consuming and convoluted for a real gmat question.

KarishmaB · Answer

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.

Carcass · Answer

I agree with you but form the question is still cumbersome. By the way, awesome explanation

as usual from you

MathRevolution · Answer

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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