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John can build a wall in 30 days and Peter can demolish the same wall

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Sarasai019
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John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   Updated on: 27 Aug 2023, 03:23
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John can build a wall in 30 days and Peter can demolish the same wall in 40 days.If they work on alternate days with John starting the job on the 1st day , then in how many days will the wall be built for the first time?

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233

Originally posted by Sarasai019 on 26 Sep 2018, 06:01.
Last edited by Carcass on 27 Aug 2023, 03:23, edited 1 time in total.
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   26 Sep 2018, 13:09
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Sarasai019 wrote:
John can build a wall in 30 days and Peter can demolish the same wall in 40 days.If they work on alternate days with John starting the job on the 1st day , then in how many days will the wall be built for the first time?

I get 240 as the answer. But certain people say its 233. Not sure about the right answer to this. Any help solving this is appreciated! Thanks :)


John can build a wall in 30 days and Peter can demolish the same wall in 40 days
So, in ONE day, John can build 1/30 of the entire wall
And, in ONE day, Peter can demolish 1/40 of the entire wall

So, AFTER TWO DAYS, the portion of the wall standing = 1/30 - 1/40 = 1/120

So, AFTER TWO DAYS, 1/120 of the wall is built (and remains standing)
So, after FOUR DAYS, 2/120 of the wall is built (and remains standing)
And after SIX DAYS, 3/120 of the wall is built (and remains standing)
.
.
.
And after 232 DAYS, 116/120 of the wall is built (and remains standing)

On DAY 233, it's John's turn to build.
Remember that, in ONE day, John can build 1/30 of the entire wall
In other words, in ONE day, John can build 4/120 of the entire wall

So, after 232 DAYS, 116/120 of the wall was built, and on the 233rd day, John built the remaining 4/120 of the wall.
So, WALL COMPLETE!!

Answer: 233

Cheers,
Brent
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Sarasai019
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   27 Sep 2018, 06:44
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Thanks much for such a detailed and clear explanation, Sir! I just learnt from internet about a technique for solving time and work problems. It actually worked out for most of the problems I solved but it was otherwise with this one problem. I'm just curious to learn where did I go wrong in either understanding or applying this concept. So, what I did using that concept is this - " Assume total work to be 120 units. So, John will do 40 units of work per day and Peter will (un)do 30 units of work per day. So, in a span of two days, 10 units of work would be done. This implies, in a span of 20 days, 100 units of work would be completed. On the 21st day, it would be John's turn and he can do 40 units/day but we want just 20 units/day, therefore, the work can be completed in 20.5 days". I am still unclear as to why this particular method flunked or how to apply the same method of assuming a value for work for this type of question! Thanks in advance! :)
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   13 Oct 2018, 06:20
Thanks for your solution. But the solution is time consuming. Is there shortcut solution ?
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   30 Oct 2018, 19:42
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Sarasai019 wrote:
John can build a wall in 30 days and Peter can demolish the same wall in 40 days.If they work on alternate days with John starting the job on the 1st day , then in how many days will the wall be built for the first time?

I get 240 as the answer. But certain people say its 233. Not sure about the right answer to this. Any help solving this is appreciated! Thanks :)



Hi....

Two days work is \(\frac{1}{30}-\frac{1}{40}=\frac{1}{120}\)
Let they work for X set of two days and then last day John works and does 1/30 work so as to complete the work
So \(\frac{X*1}{120}+\frac{1}{30}\geq{1}.......X+4\geq{120}......X\geq{116}\)
So number of days = 2*X+1=2*116+1=232+1=233

Hope this helps as a shorter method.
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   13 Jul 2019, 22:07
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To have the wall built on John's day, So the completion day falls on John, i.e. 1-(1/30) or 29/30 work will be done through the building and demolishing process.
We see that, the two persons net work in two days =1/120.
So, they complete ( alternately ) 1/120 part of the work in 2 days
They do the whole ( 1) part of the work in 2*120 days.
likewise, they do 29/30 part of the work in 2*120*29/30=232 days.
So, Total days taken 232+1 ( the last day of John)= 233 Days
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   13 Aug 2019, 23:23
Sarasai019 wrote:
Thanks much for such a detailed and clear explanation, Sir! I just learnt from internet about a technique for solving time and work problems. It actually worked out for most of the problems I solved but it was otherwise with this one problem. I'm just curious to learn where did I go wrong in either understanding or applying this concept. So, what I did using that concept is this - " Assume total work to be 120 units. So, John will do 40 units of work per day and Peter will (un)do 30 units of work per day. So, in a span of two days, 10 units of work would be done. This implies, in a span of 20 days, 100 units of work would be completed. On the 21st day, it would be John's turn and he can do 40 units/day but we want just 20 units/day, therefore, the work can be completed in 20.5 days". I am still unclear as to why this particular method flunked or how to apply the same method of assuming a value for work for this type of question! Thanks in advance! :)


The mistake is that John would do +4 units of work everyday,while Peter would do -3units.So,combined they do 1 unit of work in 2 days.For 116 units of work , they'd take 232days, then john would do +4 units on the 233rd day, making it 120units.
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   30 Mar 2021, 22:34
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Sarasai019 wrote:
John can build a wall in 30 days and Peter can demolish the same wall in 40 days.If they work on alternate days with John starting the job on the 1st day , then in how many days will the wall be built for the first time?

Show: ::
233


John has completed \(\frac{1}{30}\) of the work on the first day.

Work Left = \(1 - \frac{1}{30} = \frac{29}{30}\)

Combined rate of John and Peter for \(2\) days= \(\frac{1}{30} - \frac{1}{40} = \frac{1}{120}\)

Time to finish leftover work = \((2)\frac{29}{30}/\frac{1}{120}\)
\(= \frac{(2)(29)(120)}{(30)} = 232\)

Therefore, total time required = \(1 + 232 = 233 days\)
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   08 Apr 2021, 05:39
querry , i used W=r*t concept but i dont get answer,
what i did here follows as--
1/30-1/40=0.00833=combined rate
then, let assume W=1
and w=combined rate*time
1=0.00833*time
time=120.48
so my question, where i made mistake?
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   25 Jul 2023, 02:56
I find it difficult to understand work and rate problems. I learnt some from youtube and I wanted to find work and rate formulas or theory part ie explanation here but there's not much I could find. Can someone please comment the links for work and rate question forums or theory explanation forums? It would be a great help!
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   25 Jul 2023, 03:21
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If you see this link that you find in the landing page https://gre.myprepclub.com/forum/free-m ... 18796.html

Follow this link which is quant section on top https://gre.myprepclub.com/forum/gre-ma ... 29264.html

If you follow our daily challenge topic-wise questions here https://gre.myprepclub.com/forum/gre-qu ... ml#p107385 you will see that every single question to practice is chained to the specific theory which is here https://gre.myprepclub.com/forum/gre-ti ... 24922.html

I do not know how to highlight more the countless resources we do have :(
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink] New post   25 Jul 2023, 03:34
Thank you so much!!
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