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There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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10 Jul 2011, 20:35
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There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members. A.1/4 B.1/5 C 1/6 D 1/7 E 1/8
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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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10 Jul 2011, 23:11
Alchemist1320 wrote: There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.
A.1/4 B.1/5 C 1/6 D 1/7 E 1/8 Just plug in Assuming there are 100 employees 25% are PT = 25 75% FT = 75 Assume that the total number of hrs FT employees have to work = 10 PT will work = 3/5*10 = 6 since the wages are same , there will no affect on ratios total number of hrs FT employees work = 75*10 = 750 PT = 25*6 = 150 now the ratio is 150/900 = 1/6



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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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02 Aug 2015, 11:55
25 PT & 75 FT
Total time taken by PT members for their work  3 Total time taken by FT members for their work  5
Wages were all same for both.
Total wages for PT members  3*25 = 75 Total wages for FT members  5*75 = 375
Ratio of total wages of part time members to Total wage of all members = 75:(75+375) = 1:6



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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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09 Jan 2016, 12:10
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.



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There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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16 Jan 2016, 17:43
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



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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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18 Jan 2016, 11:53
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
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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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17 Feb 2017, 05:33
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 \(PT/Total=\frac{$750}{$4500}=\frac{1}{6}\)



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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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23 Feb 2017, 10:26
Alchemist1320 wrote: There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.
A.1/4 B.1/5 C 1/6 D 1/7 E 1/8 We can let the total staff members = x. Thus, 0.25x = parttime and 0.75x = fulltime. We can let f = the work time of each fulltime member; thus, the work time of each parttime member is (3/5)f = 0.6f. The total wage of the parttime members is (0.25x)(0.6f) = 0.15xf The total wage for fulltime 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 parttime members to total wage of all members is: 0.15xf/0.9xf = 15/90 = 1/6 Answer: C
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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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11 Mar 2017, 09:25
I reached the 1/6 solution fast applying smart numbers



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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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11 Mar 2017, 13:44
Alchemist1320 wrote: There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.
A.1/4 B.1/5 C 1/6 D 1/7 E 1/8 25*3/5=15 75*5/5=75 15+75=90 15/90=1/6 C



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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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04 Aug 2017, 08:00
Alchemist1320 wrote: There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.
A.1/4 B.1/5 C 1/6 D 1/7 E 1/8 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
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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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26 May 2018, 16:29
Alchemist1320 wrote: There are 2 kinds of staff members in a certain company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.
A.1/4 B.1/5 C 1/6 D 1/7 E 1/8 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 parttime workers. 3/8  hours of parttime workers, 5/8  hours of fulltime workers (3/8=3/5 * 5/8) 1  total namber of workers 1  total number of hours



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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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26 May 2018, 19:17
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 \(\frac{1}{6}\)
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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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26 May 2018, 19:47
CAMANISHPARMAR wrote: 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)



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Re: There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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26 May 2018, 19:52
DharLog wrote: CAMANISHPARMAR wrote: 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!
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There are 2 kinds of staff members in a certain company, PART TIME AND [#permalink]
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26 May 2018, 21:19
CAMANISHPARMAR wrote: 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 \(\frac{1}{6}\) Algebraically: Let the total number of employees be \(x\) Therefor parttime 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 prethinking and would have realized that these variables will have no effect on the final answer and will cancel out each other.
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