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

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Joined: 05 Jul 2016
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Concentration: Finance, Nonprofit
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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 2016, 19:42
let's strictly apply the equation "R*T=W" for R=rate, T=time and W=work

R * T = W
(1) 9V1*20*7.5=10, we will get V1=1/135
(2) 12V2*T*6=20

And according to the description "2 persons in the latter case do work as much as 3 men in the former", we know that V1/V2=2/3. Thus we will get V2=3V1/2

Combining V1=1/135 and V2=3V1/2, we will get V2=1/90 which could be put into (2)

Finally, we will see that 12*1/90*T*6=20 and T is 25.

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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29 Aug 2016, 10:08
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

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

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18 Sep 2016, 05:16
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

This is how I usually do these kinds of problems. Not sure if it will make sense to you guys or not. I do it in multiple steps and at each step I ask myself if the operation in current step is going to increase or decrease the item that we are trying to determine. In this present question at each step we will try too determine if the current operation is going to increase or decrease the number of days. If it increase then I multiply if it decreases then I divide with the factor that changes from the previous step..
I suppose I'm not able to convey this clearly so lets show with the following example

9 persons---10 tv---7.5 hr---20days
1person--------"--------------- 20*9 days ( 1 person will take more time so I multiply)
12 persons--------"----------- 20*9/12 ( 12 persons will take less time so I divide by the factor, if you are comfortable you can always combine the above two steps)
-------"--------20 tv------"---- 20*9*20/(12*10) days
-------------"-----------6 hr---- 20*9* 20 * 7.5 /(12*10*6) = 37.5 days

on similar logic if 3 men in former case work as much as men in later case, certainly our second case workers work faster hence the job will get completed earlier hence out of the two options we have i.e. multiple with the ratio 2/3 or ratio 3/2 , we will go ahead and multiply with 2/3 since that will reduce the number of days.
So answer = 37.5 *2/3 = 25.

Not sure if I was able to explain that clearly.
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days  [#permalink]

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14 Dec 2018, 00:52
For those (like me) whose mind fails to bring such shortcuts during exam time:

The normal calculation method is not that tedious as you think

- 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 3/2*(1/135) => 1/90
- the rate for 12 persons is 12*(1/90)=4/30
- to assemble 20 tv it will take 20/(30/4) = 150 hours
- the number of days will be 150/6=25 days
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Re: In a TV factory 9 persons can assemble 10 tv sets in 20 days   [#permalink] 14 Dec 2018, 00:52

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