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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]

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27 Jun 2004, 14:10
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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?

A. 10
B. 12.5
C. 20
D. 25
E. 50
[Reveal] Spoiler: OA
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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27 Jun 2004, 15:44
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Hi,

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

- 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
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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27 Jun 2004, 22:54
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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: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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27 Jun 2004, 23:07
dr_sabr wrote:
Hi,

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

- 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

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

- ash
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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28 Jun 2004, 08:32
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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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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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28 Jun 2004, 10:07
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 .

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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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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28 Jun 2004, 10:22
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)

- ash
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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28 Jun 2004, 10:22
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 .

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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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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28 Jun 2004, 10:23
: x seems to be an Icon ........hehehe

the ratio is 9/x = 3/2

- ash
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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28 Jun 2004, 12:34
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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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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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03 Jul 2014, 01:31
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?

I started calculation with drafting formulas, when realised that there is a hint in this question:

1 step. Given the productivity coefficient of 2/3 and number of persons in each team, actual productivity of the whole second team (12 persons) appears to be twice greater than the actual productivity of the whole first team (9 persons):
9 persons * 2 productivity = 18.
12 persons * 3 productivity = 36.
36/18 = 2.

2 step. At the same time, the second team should produce twice more TV sets (20/10=2).
As such, productivity and number of TV sets to be produced eliminate each other =>

3 step. The second team will spend the same number of hours:
20*7.5 = 150 h for the 1 team
150h / 6 = 25 days for the second team
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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23 Jul 2014, 23:10
Is this right way.i got the answer 25
18*40*15 =12*6*x
we get x=150

as give 1 person does 3 persons work
2 persons can do 6 persons work

150/6=25
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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23 Jul 2014, 23:44
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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?

A. 10
B. 12.5
C. 20
D. 25
E. 50

We will solve the question using the method discussed in my post here: http://www.veritasprep.com/blog/2013/02 ... variation/
Look at question 2 in the post.

But before we do that, let's make people in the two cases comparable.
2 people of latter equivalent to 3 people of former.
12 people of latter equivalent to 18 people of former.

So we see that if effect, the number of people has doubled in the latter case.

Days taken = 20 * (9/18) * (20/10) * (7.5/6) = 25 days
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In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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24 Jul 2014, 00:22
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?

A. 10
B. 12.5
C. 20
D. 25
E. 50

I used formal method to organize information:

Rate * Time = Work

1/2 * 20 = 10 for 9 people

2/3 * X = 20 for 12 people working in the same rate as 9 people. But we should multiply 2/3 to 1.5, so we get

1 * X = 20 for 12 people working 7.5 h/day. But we have only 6 hours, so we get

12/15 * X = 20, and we get 25 days

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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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24 Jul 2014, 01:31
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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?

A. 10
B. 12.5
C. 20
D. 25
E. 50

It is 20 *(9/12) * (7.5/6) *(20/10)*(2/3) = 25 days
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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01 Mar 2015, 05:06
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here we can use mandays formula.

M1D1H1/W1=M2D2H2/W2.

M1=9,D1=20,D1=15/2, W1=10.

IN second case, efficiency of 2men latter equals 3men of former.
so here 12 men becomes 2/3=12/M2 = > M2=18, D2 =X, H2= 6, W2=20

9*20*15/2 /10=18*x*6/20

x=25
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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01 Mar 2015, 17:16
hi! this is my first post but i think i got it clear and easy.

9 people (10 tvs)= 1 Job 20 days of 7hours 30 minutes
12 people (20 tvs)= 2 jobs X days of 6 hours

work on the people ratio,

if 2 people in the new group work as 3 people in the old group the relation is 12*3= 36, 36/2 =18
So we have:
18 people 2 jobs x days of 6 hours

- old group: 9 people (group A). new group 12 people productivity of 18 people (group B).

It is the doble of people and tvs for the group B, should be half of time.

group B would do 1 job = 10 tvs in half time =10 days. (days of 7:30 hours)
group B have the double of tvs to do = 2 jobs. The group B will complete the double of tvs in the same number of days that group A take to complete 1 job.

So now we understand why we will just transform 20 days of (7hours 30 minutes) to X days of 6 hours.

20 days of 7hours 30 minutes = 150 hours
150 hours divided by 6 hours at day 150/6 = 25 days.
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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01 Mar 2015, 23:51
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Basically we can do it by total man-hours.

10 TV sets take 9*20*7.5 hours
-> 10 TV sets take 1350 hours
-> 1 TV sets take 135 hours

Now, 20 TV sets will take 20*135 hours = 2700 hours
Since 12 persons are working 6 hours per day, they put up a combined 72 hours every day.

So, total days = 2700/72 = 300/8 = 37.5 days

But since in this case, 2 people work as much as 3 people, they would take 2/3rd of the time.

So, actual days = (2/3)*37.5 = 25
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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07 Mar 2015, 00:47
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The ans has to be 25 days.
I will try to do it by simple logic.
We know first, 9 men can assemble 10 TV sets in 20 days working 71/2 hours daily i.e. 150 hrs in total.
So, 9M can assemble 10 TV sets in 150 hrs.
We can say, 9M can assemble 1 TV set in 150/10=15 hrs.
Thus, 1M can assemble 1 TV set in 15X9= 135 hrs.

Now, we know 2M of latter are equivalent to 3M of former.
So if 1 M can assemble 1 TV set in 135 hrs, so 3M can do it in 135/3= 45 hrs.
This is equivalent to 2M of latter. Hence, 2M of latter case now can assemble 1 TV set in 45 hrs.
Or, 1M of latter case can assemble 1 TV set in 45X2= 90 hrs.

Now, 1 M of latter case can assemble 20 TV sets in 90X20 hrs.
Also, 12 M will take much lesser time than 1 M. So, 12 M will do the work in (90X20)/12 hrs.
We are asked to find out the no of days if they work 6 hrs daily.
So, the no of days will be (90X20)/(12X6).
This comes out be 25 DAYS.
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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29 Apr 2015, 00:51
dr_sabr wrote:
Hi,

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

- 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

A great explanation kudos to you.I was able to get the rate of one person i.e 1*/135 but then I was completely lost
Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days   [#permalink] 29 Apr 2015, 00:51

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