Difficult Math Question #48 - Ratios

Answer is 1/6

workers PT:FT = 1:3

time worked FT:PT = 1:3/5

wage per hour is w

3/5 * w/(3/5 * w + 3w) = 1/6

here's the OA:

What is the ratio of total wage of part time members to total wage of all members.

You have calculated ratio of Part time-to-Full time.

P x/4 3y/5 3xy/4*5
A 3x/4 Y + x/4 3y/5 18xy/20

Ratio= p/a= 3xy/18xy= 1/6

An easier explanation would be to use the Princeton Review's Plugin method.

As we are asked to get compute ratio, we assume the following values.
Workers Count = 100, so PT = 25 & FT = 75
Total Work Time = 15 hrs, so FT = 15, PT = 3/5 * 15 = 9
Pay per hour = $D

So total wage = 75 * 15 * D + 25 * 9 * D = 25*9*D(1+5) = 25*9*D*6
So the ratio of wage of PT to all workers = 25 * 9 * D / 25*9*D*6 = 1/6

#P : #F = 1:3

Sal_ P : Sal_F = 3:5

Hence the Total salary : salary P = 1:6

C.1/6
when a question contains only ratios or percentage, better substitute values
total number=100
part time=25
full time=75
part time work hours 3
full time work hours=5
wage per hour=10
part time total wage=10*3*25=750
full time total wage=10*5*75=3750
750/(3750+750)=1/6

takegmat wrote:An easier explanation would be to use the Princeton Review's Plugin method.

As we are asked to get compute ratio, we assume the following values.
Workers Count = 100, so PT = 25 & FT = 75
Total Work Time = 15 hrs, so FT = 15, PT = 3/5 * 15 = 9
Pay per hour = $D

So total wage = 75 * 15 * D + 25 * 9 * D = 25*9*D(1+5) = 25*9*D*6
So the ratio of wage of PT to all workers = 25 * 9 * D / 25*9*D*6 = 1/6

sorry for a simple question but could you explain the bolded part? How do you do that?

A lot of different approaches to the problem, I did the same thing as tohellandback