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Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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Updated on: 17 Jan 2019, 20:38
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66% (01:56) correct 34% (01:43) wrong based on 95 sessions
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Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do? A) 1/4 B) 1/6 C) 1/8 D) 13/6 E) 6/13
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Originally posted by Manat on 17 Jan 2019, 18:09.
Last edited by Bunuel on 17 Jan 2019, 20:38, edited 1 time in total.
Renamed the topic and edited the question.



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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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17 Jan 2019, 18:16
Manat wrote: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?
A) 1/4 B) 1/6 C) 1/8 D) 13/6 E) 6/13 Are you getting B ?? = 4 / 24 = 1 / 6
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17 Jan 2019, 19:07
Yes i got B. if the question had mentioned what part of the work is done in 1 hour, then i would have chosen 6/13 the OA. Confused
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17 Jan 2019, 19:19
Manat wrote: Yes i got B. if the question had mentioned what part of the work is done in 1 hour, then i would have chosen 6/13 the OA. Confused
Posted from my mobile device IMO, the question has not asked that. Lets see if someone else adds something to this.
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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17 Jan 2019, 19:46
chetan2u Bunuel :Could you please confirm if OA is correct?



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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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17 Jan 2019, 20:45



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17 Jan 2019, 20:51
Manat wrote: chetan2u Bunuel :Could you please confirm if OA is correct? The OA is correct.. Each working together, the work can be done in (1/4)+(1/6)+(1/8)=13/24th work in one hour, so complete work in 24/13 hour.. Now the fastest machine can do the work in 4 hours so in 24/13 hours he can do (1 hour work)*(number of hours)=(1/4)*(24/13)=6/13.. Also how can fastest machine do just 1/6 of work, which means someone will do more than 1/6 of work. But fastest should do the maximum portion of work...
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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18 Jan 2019, 03:43
Manat wrote: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?
A) 1/4 B) 1/6 C) 1/8 D) 13/6 E) 6/13 total rate of three machines = 1 so part of rate done by each machine = 13/24 and total time : 24/13 work done by fastest machine would be the one which has lowest hrs i.e 4 and rate : 1/4 so work of machine = rate * time = 24 /13*1/ 4= 6/13 IMO E
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Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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18 Jan 2019, 04:13
Really you can answer this question using the provided options and logic without ever doing any math.
There are 3 machines completing 1 task, if all machines worked at the same pace they would each complete 1/3 of the task. We know that 1 of the machines is the fastest and therefore will complete more than 1/3rd of the task because it is more productive than the others. This immediately eliminates A, B, and C as all are less than 1/3. D is eliminated because a machine cannot complete more than 100% of the task. Thus E is the only possible answer.
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18 Jan 2019, 06:35
Manat wrote: Yes i got B. if the question had mentioned what part of the work is done in 1 hour, then i would have chosen 6/13 the OA. Confused
Posted from my mobile device Afterall the OA was correct. I again took an attempt at it, I solved it at paper this time( last time i didn't) Work = rate * time Total Time = 1/4 + 1/6 + 1/ 8 = 13/24 Took W as 1 Now if we take work as W, then rate = 24 / 13 Now what part of the finished work does the fastest machine do will be rate * time => 24/13 * 1/4 => 6/13
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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19 Jan 2019, 10:30
given that each machine completes the work in that many hours. not the rate of work done by each machine. rate of work done by each machine A 1/4 B1/6 C1/8
TOTAL work done by three machines in one hour is equal to combined rates of work 1/4+1/6+1/8=13/24
fastest machine is the one which completes the work in shortest time i.e. 1/4
asked about the part by whole (1/4)/(13/24)=6/13



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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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20 Jan 2019, 08:04
Manat wrote: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectively. If all the 3 machines work together to finish the work, then what part of the finished work does the fastest machine do?
A) 1/4 B) 1/6 C) 1/8 D) 13/6 E) 6/13 Let the total work be 24 (LCM of 4,6 & 8) Efficiency of the 3 machines are 6 , 4 & 3 Thus, part of the finished work done by the fastest worker is \(\frac{6}{( 6+ 4 + 3)} = \frac{6}{13}\) Fastest Worker = Worker having the highest efficiencyThus, Answer must be (E)
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Re: Three machines can finish a work in 4 hrs, 6 hrs and 8 hrs respectivel
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22 Jan 2019, 09:06
time is taken by machines 4, 6 & 8 hours to complete a task individuality it means their efficiencies are 6 / 4 / 3 (Because LCM is 24 for 4,6 and 8 and 24 is further divided by 4 /6/ 8 )
Hence, 6/6+4+3 gives 6/13 (a portion of the fastest machine)




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