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.