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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, 03:44

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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

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

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

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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 =1-22/24=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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Please hit kudos button below if you found my post helpful..TIA

Jack and Jill working separately complete a work in 8 days and 12 days [#permalink]

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21 Aug 2017, 08:22

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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) _________________

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

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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Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions