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In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
27 Jun 2004, 13:10

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Difficulty:

95% (hard)

Question Stats:

53% (03:33) correct
47% (02:58) wrong based on 100 sessions

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?

Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
27 Jun 2004, 14:44

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.

Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
27 Jun 2004, 21:54

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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!

Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
27 Jun 2004, 22:07

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 _________________

ash
________________________
I'm crossing the bridge.........

Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
28 Jun 2004, 07:32

1

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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")

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

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 _________________

-Genius is one percent inspiration, and ninety-nine percent perspiration.

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

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.

Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
03 Jul 2014, 00:31

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

Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
23 Jul 2014, 22:44

Expert's post

2

This post was BOOKMARKED

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?

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 _________________

In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
23 Jul 2014, 23:22

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

Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days [#permalink]
24 Jul 2014, 00:31

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?

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 _________________