There are 2 kinds of staff members in a certain company, PART TIME AND

i tried to pick numbers rather than dive into algebra...
suppose we have total 20 workers: 5 workers part time, 15 workers full time.
suppose full time work 10 hours, part time 6 hours.
suppose pay is 1$/hour
we then have: 5*6*1=30$ - pay for part time workers
and we have: 15*10*1=150$ - pay for full time workers.

total pay - 150+30=180$.

now, we need to have the ratio of pay for part time to total pay
30/180=1/6.

let 1 and 3=number of part time and full time workers respectively
let 3 and 5=number of hours per part time and full time worker respectively
(1)(3)=3 total part time worker hours
(3)(5)=15 total full time worker hours
3+15=18 total worker hours
assuming equal hourly pay, total wage ratio=3/18=1/6

Hi All,

This question is a 'lift' of an OG question:

GMAT2016: Problem Solving #175, page 177
OG13/GMAT2015: Problem Solving #151, page 173

GMAT assassins aren't born, they're made,
Rich

For me the easiest way to understand this problem was to pick numbers:

Part Time: 25 employees; 3 hours of work; 10$/h wage = Total earnings: 25*3*10=$750
Full Time: 75 employees; 5 hours of work; 10$/h wage = Total earnings: 75*5*10=$3750

PT&FT earnings: $750+$3750=$4500
\(PT/Total=\frac{$750}{$4500}=\frac{1}{6}\)

We can let the total staff members = x. Thus, 0.25x = part-time and 0.75x = full-time.

We can let f = the work time of each full-time member; thus, the work time of each part-time member is (3/5)f = 0.6f.

The total wage of the part-time members is (0.25x)(0.6f) = 0.15xf

The total wage for full-time members is 0.75xf.

Thus, the total wage for all members is 0.75xf + 0.15xf = 0.9xf, and the ratio of total wage of part-time members to total wage of all members is:

0.15xf/0.9xf = 15/90 = 1/6

Answer: C

I reached the 1/6 solution fast applying smart numbers

25*3/5=15
75*5/5=75
15+75=90
15/90=1/6
C

Let the total number of members be N
So part time members = .25N & Full time members = .75N

Let the wage be W per hour which is same for both full time and part time members.

Let the work time be T hours for full time members so it will be 3T/5 hours for part time members.

Ratio of total wage of part time members to total wage of full time members = .25N * W * (3T/5) / .75N * W * T = 1/5
Ratio of total wage of part time members to total wage of all the members = 1/(1+5) = 1/6

Answer C

Can you tell me where is a mistake in this approach?

The answer = (1/4 * 3/8) / (1 * 1) = 3/32
1/4 - 25% of part-time workers.
3/8 - hours of part-time workers, 5/8 - hours of full-time workers (3/8=3/5 * 5/8)
1 - total namber of workers
1 - total number of hours

Pick a smart number say 100
Part time - 25
Full time - 75

Let the number of hours required to be worked in a day are 10 & wage rate per hour be 10.
Total wage of part time = 25*10*3/5*10 = 1500
Total wage of full time = 75*10*10 = 7500
The required ratio of total wage of part time members to total wage of all members = \(\frac{1500}{1500+7500}\)
which is equal to \(\frac{1}{6}\)

No, no, thanks)

Of course I understand what guys have written here before. It is a good solution.

But I wanted to do it globally (without picking numbers), and I know that my logic is correct, but obviously I miss something, because get another answer (no option has it)

Nice to know that you get it and you want to do it algebraically. Maybe my solution is useful to other users who often solve questions posted by other users.

All the best!

Algebraically:-
Let the total number of employees be \(x\)
Therefor part-time will be \(\frac{x}{4}\)
fulltime will be \(\frac{3x}{4}\)

Let the number of hours required to be worked in a day are y hours & wage rate per hour be $z per hour.

Total wage of part time = \(\frac{x}{4}*y*\frac{3}{5}*z\) = \(\frac{3xyz}{20}\)\(\)
Total wage of full time = \(\frac{3x}{4}\) \(* y * z =\)\(\frac{3xyz}{4}\)\(\)

The required ratio of total wage of part time members to total wage of all members = \(\frac{3xyz}{20}\)\(\) divided by (\(\frac{3xyz}{20}\)\(\) + \(\frac{3xyz}{4}\)\(\))

which is equal to \(\frac{3xyz}{18xyz} = \frac{1}{6}\)

PS: Intuitively one could ignore the variables y and z if they did some pre-thinking and would have realized that these variables will have no effect on the final answer and will cancel out each other.

Given:
1. There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME.
2. 25 percent of the total members are PART TIME members others are FULL TIME members.
3. The work time of part time members is 3/5 of the full time members.
4. Wage per hour is same.

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

Let the total number of staff members be x
and let the wage per hour be y

1. There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME.
2. 25 percent of the total members are PART TIME members others are FULL TIME members.
3. The work time of part time members is 3/5 of the full time members.
4. Wage per hour is same.

Total wages of PART TIME members = (25%x) * (3/5)*y = (1/4 * 3/5) xy = (3/20) xy
Total wages of FULL TIME members = 75%x *y = (3/4) xy

The ratio of total wage of part time members to total wage of full time members = \(\frac{\frac{3}{20}}{\frac{3}{4}} = \frac{4}{20} = \frac{1}{5}\)
The ratio of total wage of part time members to total wage of all members =\(\frac{1}{6}\)

IMO C

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