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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, 21:38
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55% (hard)
Question Stats:
63% (01:54) correct 37% (01:50) wrong based on 113 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?
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17 Jan 2019, 21:45
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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
The combined rate of the three machines is 1/4 + 1/6 + 1/8 = 13/24 work/hour. So, working together they can do the job in 24/13 hours. In this time the fastest machine, the one that can do the job in 4 hours, would have done 1/4*24/13 = 6/13 part of the job (job done = rate*time).
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17 Jan 2019, 19:16
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, 21:51
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Manat wrote:
chetan2uBunuel :-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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18 Jan 2019, 04:43
1
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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18 Jan 2019, 05:13
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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19 Jan 2019, 11:30
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 B-1/6 C-1/8
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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20 Jan 2019, 09:04
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 efficiency
Thus, Answer must be (E) _________________
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Abhishek....
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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, 10:06
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)
gmatclubot
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22 Jan 2019, 10:06
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63% (01:54) correct 
