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Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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Updated on: 21 Aug 2017, 05:30
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Jack and Jill working separately complete a work in 8 days and 12 days respectively. If they work on alternate days starting with Jill on the first day, in how many days will the work be completed? A) 9 1/2 days B) 9 2/3 days C) 10 days D) 10 8/12 days E) 12 days kudos if it helps.
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Re: Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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21 Aug 2017, 03:57



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Re: Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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21 Aug 2017, 04:02
pushkarajnjadhav wrote: Jack and Jill working separately complete a work in 8 days and 12 days respectively. If they work on alternate days starting with Jill on the first day, in how many days will the work be completed?
A) 9 1/2 days B) 9 2/3 days C) 10 days D) 10 8/12 days E) 12 days Total work done by Jack and Jill in two days =1/12+1/8=5/24 So, 5/24 of total work is done in 2 days so 20/24 of total work will be done in 8 days.. Jill will work on 9th day and further complete...1/12 or we can say 2/24 of total work on 9th day.. So total work done till 9th day will be 20/24+2/24=22/24...remaining work =122/24=2/24.. as Jack does 1/8 or 3/24 work in 1 day, remaining 2/24 work will be done by Jack in 2/3 days ... So total 9 2/3 days..its 600 level
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Re: Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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21 Aug 2017, 05:26
Jack : Jill Days: 8 : 12 LCM(8,12) = 24 So let 24 be the total work. Rate: 3 : 2 24 total work divided by days to finish work gives rate.
Now, In 1 day Jack can finish 3 parts of total work and Jill can finish 2 parts of total work.
So, If Jill starts the work and Jack follows him next day then in 2 days they finish 5 parts of work.
Our total work is 24. So 24/5=4(only proper quotient). Hence in 4X2= 8days they finish 20 parts of work.
Remaining part = 4. Again Jill will start and finish his 2 part in 1 day. So in 9 days 22 parts of work is finished.
Remaining part = 2. Jack's turn who finish 3 parts of work in 1 day. So 2 part is finished in 2/3 day.
Hence Total days required = 8 + 1 + 2/3 = 9 2/3.
Although this solution seems to be lengthy but once understood then it is very easy to use.



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Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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21 Aug 2017, 08:22
Let the total number of units be 96.
Since Jack completes the work in 8 days, he must be completing 12 units/daySimilarly, since Jill completes the work in 12 days, he must be completing 8 units/dayIt has been given that they work alternate days with Jill starting the work on the first day In a span of 2 days, both Jack and Jill will cover 20 units of the workSo they would have completed 80 units in 8 days and on the 9th day Jill completes 8 units(making total 88 units) Now, for the remaining 8 units, Jack would have to work \(\frac{2}{3}\) day. The total time taken to complete the work is \(9\frac{2}{3}\) days (Option B)
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Re: Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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31 Aug 2017, 03:46
pushpitkc wrote: Let the total number of units be 96.
Since Jack completes the work in 8 days, he must be completing 12 units/day Similarly, since Jill completes the work in 12 days, he must be completing 8 units/day
It has been given that they work alternate days with Jill starting the work on the first day In a span of 2 days, both Jack and Jill will cover 20 units of the work So they would have completed 80 units in 8 days and on the 9th day Jill completes 8 units(making total 88 units)
Now, for the remaining 8 units, Jack would have to work \(\frac{2}{3}\) day.
The total time taken to complete the work is \(9\frac{2}{3}\) days(Option B) Best and very comprehensive approach. Thanks...It helps
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Re: Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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31 Aug 2017, 07:17
lets take total work = 24 unit (it can be easily divisible by 8 and 12) jack = 24/8 = 3 unit /day Jill = 24/12 = 2 unit /day To complete 24 unit alternate days. 2U,3U,2U,3U,2U,3U,2U,3U,2U =22 unit in 9 days ...
Rest Jack have to finish He will take 2/3 days total 9 2/3



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Re: Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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02 Sep 2017, 07:21
pushkarajnjadhav wrote: Jack and Jill working separately complete a work in 8 days and 12 days respectively. If they work on alternate days starting with Jill on the first day, in how many days will the work be completed?
A) 9 1/2 days B) 9 2/3 days C) 10 days D) 10 8/12 days E) 12 days Jack’s rate is 1/8 and Jill’s rate is 1/12. In the first day, Jill completes 1/12 of the job. In the second day, Jack completes 1/8 of the job. Thus, in the first two days, Jill and Jack complete 1/12 + 1/8 = 2/24 + 3/24 = 5/24 of the job. If we multiply the amount of work done in two days by 4, we will have 20/24 of the job completed by Jill and Jack in 8 days. On the ninth day, Jill completes another 1/12, or 2/24, of the job. So, the total amount of work done so far is 22/24 of the job. We need the last 2/24 of the job to be completed, and it will be completed by Jack, whose rate is 1/8. Since (2/24)/(1/8) = 16/24 = 2/3, Jack needs only 2/3 of a day to complete the last 2/24 of the job. Thus, to complete the entire job, they need 9 2/3 days. Answer: B
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Re: Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]
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05 Sep 2017, 17:47
pushkarajnjadhav wrote: Jack and Jill working separately complete a work in 8 days and 12 days respectively. If they work on alternate days starting with Jill on the first day, in how many days will the work be completed?
A) 9 1/2 days B) 9 2/3 days C) 10 days D) 10 8/12 days E) 12 days
kudos if it helps. Jack’s rate is 1/8 and Jill’s rate is 1/12. In the first day, Jill completes 1/12 of the job. In the second day, Jack completes 1/8 of the job. Thus, in the first two days, Jill and Jack complete 1/12 + 1/8 = 2/24 + 3/24 = 5/24 of the job. If we multiply the amount of work done in two days by 4, we will have 20/24 of the job completed by Jill and Jack in 8 days. On the ninth day, Jill completes another 1/12, or 2/24, of the job. So, the total amount of work done so far is 22/24 of the job. We need the last 2/24 of the job to be completed, and it will be completed by Jack, whose rate is 1/8. Since (2/24)/(1/8) = 16/24 = 2/3, Jack needs only 2/3 of a day to complete the last 2/24 of the job. Thus, to complete the entire job, they need 9 2/3 days. Answer: B
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