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In a TV factory 9 persons can assemble 10 tv sets in 20 days

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In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink] New post 27 Jun 2004, 13:10
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In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?
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Re: PS Working together [#permalink] New post 27 Jun 2004, 14:44
Hi,

We can solve the question if we take it step by step :idea: .

- the number of hours is 7.5*20=150
- the rate for the 9 persons is 10tv/150hours =>1/15
- the rate for one person is (1/15)/9 => 1/135
- the now rate of new workers is 2 men to 3 men => the new rate will be 2/3*(1/135) => 2/405
- the rate for 12 persons is 12*(2/405)=8/135
- to assemble 20 tv it will take 20/(8/135) = 168.75 hours
- the number of days will be 168.75/6=28.125 days

I believe that this is the safest way to solve this problem, but I admit it is time consumer. if anyone know a better way pls share us.

Correct me if I am wrong :wink:
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Re: PS Working together [#permalink] New post 27 Jun 2004, 21:54
boksana wrote:
In a TV factory 9 persons can assemble 10 tv sets in 20 days of 7 1/2 working hours. How long will it take for 12 persons to assemble 20 tv sets working 6h per day, it being given that 2 persons in the latter case do work as much as 3 men in the former?


:-) Similar question was given to me on my job interview in a management consulting firm! Oksana, you are great!

OK, let's go on to the solution:

12 X 6 -> 20, X - ?

9(former) 20 7.5 -> 10 <=> 6(latter) 20 7.5 -> 10 => (12/6)*(X/20)*(6/7.5) = 20/10 => X = 25.

25 days.
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Re: PS Working together [#permalink] New post 27 Jun 2004, 22:07
dr_sabr wrote:
Hi,

We can solve the question if we take it step by step :idea: .

- the number of hours is 7.5*20=150
- the rate for the 9 persons is 10tv/150hours =>1/15
- the rate for one person is (1/15)/9 => 1/135
- the now rate of new workers is 2 men to 3 men => the new rate will be 2/3*(1/135) => 2/405
- the rate for 12 persons is 12*(2/405)=8/135
- to assemble 20 tv it will take 20/(8/135) = 168.75 hours
- the number of days will be 168.75/6=28.125 days

I believe that this is the safest way to solve this problem, but I admit it is time consumer. if anyone know a better way pls share us.

Correct me if I am wrong :wink:


I think there is a slight glitch in your calculation of the rate of work for the new person.

If P1 does 1/135 work in a day ........p2 should be doing 3/2 * 1/135 work in a day.

If you continue with that then you get 25 days as the result.

To save time......there is no need to do all intermediate calculations. In work time methods .........values cancel out most of the time. Of course then one has to be careful

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Re: PS Working together [#permalink] New post 28 Jun 2004, 01:18
[quote="ashkg"]

If P1 does 1/135 work in a day ........p2 should be doing 3/2 * 1/135 work in a day.[/quote]

Thnaks for correcting me ash. :-D
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 [#permalink] New post 28 Jun 2004, 07:08
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Can you elucidate your solution in detail
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 [#permalink] New post 28 Jun 2004, 07:32
pakoo wrote:
emmanuel

Can you elucidate your solution in detail


OK, pakoo. Look, 9 former workers do the same job as 6 latter workers ceteris paribus (in the same # of hours, same # of days), because their productivities relate to each other at a ratio of 3:2.

Then 6 "productive" workers make 10 TV sets in 20 days of 7.5 hours/day.

How many TV sets would make 12 "productive" workers in 20 days working 6 hours/day?

Number of TV sets depends on

a) time in days(positively),

b) duration of each working day(positively),

=> total productivity ~ WORKERS*DAYS*HOURS. (here "~" means "is proportional to")

We know that 10 ~ 6*20*7.5

And we know that 20 ~ 12*DAYS*6.

=> dividing first by the second we get DAYS = 25.
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 [#permalink] New post 28 Jun 2004, 09:07
Emmanuel wrote:
OK, pakoo. Look, 9 former workers do the same job as 6 latter workers ceteris paribus (in the same # of hours, same # of days), because their productivities relate to each other at a ratio of 3:2.

Then 6 "productive" workers make 10 TV sets in 20 days of 7.5 hours/day.


Emmanuel, you seems to have a brilliant way in solving math questions :-D .

I just want to make sure how did you get 6 latter workers. did you multiply the ratio of 3:2 by the ratio between the number of workers?

12/9*3/2=12/6? can you explain why?

Thanks
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 [#permalink] New post 28 Jun 2004, 09:22
9:x :: 3:2

this is the ratio that will give the new number of people required (x) for doing the old job = 6.

after that u got to carry on the normal way.( unitary method)

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 [#permalink] New post 28 Jun 2004, 09:22
dr_sabr wrote:
Emmanuel wrote:
OK, pakoo. Look, 9 former workers do the same job as 6 latter workers ceteris paribus (in the same # of hours, same # of days), because their productivities relate to each other at a ratio of 3:2.

Then 6 "productive" workers make 10 TV sets in 20 days of 7.5 hours/day.


Emmanuel, you seems to have a brilliant way in solving math questions :-D .

I just want to make sure how did you get 6 latter workers. did you multiply the ratio of 3:2 by the ratio between the number of workers?

12/9*3/2=12/6? can you explain why?

Thanks


Yes, I did. :-) Such things should be done very quickly on your actual GMAT... That's why it is so important to multiply, add, subtract and divide fractions quickly.

Yes, I multiplied 9 by 2/3 and got 6 workers. 9:6 = 3:2.
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 [#permalink] New post 28 Jun 2004, 09:23
: x seems to be an Icon ........hehehe

the ratio is 9/x = 3/2

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 [#permalink] New post 28 Jun 2004, 11:34
Although this problem was already solved, i am adding my calculations as an extra explanation:

since 2 persons in the latter case do work as much as 3 men in the former,
12 latter = 18 former.

So let's see how many hours it will take 18 former to complete the job and then divide the sum by 6 to get the number of days.

9 Workers, 20*7.5 hours, 10 T.V
9 Workers, 20*7.5*2 hours, 20 T.V
18 Workers, (20*7.5*2)/2 hours, 20 T.V

(20*7.5*2)/2 = 150.
150/6 = 25.
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 [#permalink] New post 28 Jun 2004, 13:14
I also got 25, although my way took me slightly over 3 minutes to solve the problem
  [#permalink] 28 Jun 2004, 13:14
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