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

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

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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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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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New post 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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The question seems slightly heavy because of the number of data points given. Let me simplify it by presenting a stepwise detailed solution

Given
We are given information about two sets of people working. In the first case 9 people assemble 10 TV sets in 20 days working 7.5 hours/day. In the second case we are asked to find the time taken by 12 people to assemble 20 TV sets working 6 hours/day. We are also told that the amount of work done by 2 people in second case is equal to the amount of work done by 3 people in the first case.

Let's see how can we break down this question into simpler bits to get to our answer.

Approach
We know that Work = Rate * Time. For the first set of people we are given the amount of work done and the amount of time taken. We can use this information to find out the rate of work done by 1 person. For the next set of people we are given the amount of work to be done and are asked to find the time taken by them. For finding the time taken we will need the rate of work done by these people.

We are given a relation between the work done by the first set of people and the second set of people. We will use this information and the work rate equation to find out the rate of work done by second set of people and then the time taken by them to complete the work.

Working Out
First set of people

Work done by 9 people = 10 TV sets
Time taken by 9 people each = 7.5 hours for 20 days = \(20* 7.5\) hours

Rate of work done by 9 people = \(\frac{Work}{Time}\) = \(\frac{10}{20*7.5}\)

So, the rate of work done by 1 person \(= \frac{10}{20*7.5*9}\)

Second set of people

Work done by 12 people = 20 TV sets

We are told that 2 people in the latter case do as much work as 3 people in the former. i.e.

work done by 2 persons in the second case = work done by 3 people in the first case.

Since time taken is the same, assuming \(R_{1}\) to be the rate of 1 person in the first case and \(R_{2}\) to be the rate of 1 person in the second case we can write

\(2 * R_{2} * t = 3 * R_{1} * t\) which gives us \(R_{2} = \frac{3}{2} * R_{1} = \frac{3}{2} * \frac{10}{20*7.5*9}\) for 1 person

Rate of work done by 12 people \(= 12 * \frac{3}{2} * \frac{10}{20*7.5*9}\)

Let's assume the number of days it took 12 people to assemble 20 TV sets be \(x\). As the people worked for 6 hours daily,time taken by 12 people each =\(6x\) hours.

Putting the above information in the equation Work = Rate * Time, we get

\(20 = 12 * \frac{3}{2} * \frac{10}{20*7.5*9} * 6x\)

\(x = 25\) days

Hope this helps :)

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

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New post 09 Jul 2015, 23:48
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jayanthjanardhan wrote:
VeritasPrepKarishma wrote:
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



Hi karishma,

Can you please explain how you got (20/10) in the above expression?


In the former case, they assemble 10 tv sets and in the latter case they assemble 20 tv sets. Since they assemble more tv's in the second case, days taken will be more so we multiply previous days taken (20) by 20/10.
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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Here's my approach -

Efficiency of 9 former men = 6 latter men
=> 6 latter men make 10 sets in 150 hours
=> 12 latter men make 20 sets in 150 hours = 25 days (Considering 6 hour/day)
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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GMATDemiGod wrote:
Is this right ?

- to assemble 20 tv it will take 20/(8/135) = 168.75 hours


I kept getting 337.5 as the answer here.


The questions involving multiple variables in work rate can usually be done in a single step.

But before we solve here, 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 in case 1 there were 9 people and in case 2 there were 18 equivalent people

"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?"

9 people ........10 tv sets.........20 days............7.5 hrs
18 people........20 tv sets.........?? days .............6 hrs

We start with the unknown - the number of days.
The number of days will change. They will become 20 * (9/18) * (20/10) * (7.5/6) = 25 days

20 is the original number of days which needs to be adjusted to factor in the changes in the variables.

You multiply it by 9/18 because when number of people changes from 9 to 18, the number of days will decrease. So you multiply by a number less than 1.
You multiply by 20/10 because when number of tv sets increase from 10 to 20, number of days will increase. So you multiply by a number more than 1.
You multiply by 7.5/6 because when number of hours decrease from 7.5 to 6, number of days required will increase. So you multiply by a number more than 1.

Using this logic, you don't have to worry about how each variable varies with the other. Just use the logic of increase/decrease and less than 1/more than 1.
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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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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New post 27 Jun 2004, 23:07
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: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]

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New post 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 :-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?

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

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New post 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)

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

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

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

the ratio is 9/x = 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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New post 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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New post 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
Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days   [#permalink] 23 Jul 2014, 23:10

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