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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink]
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]
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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]
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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]
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]
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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]
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]
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]
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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]
Thank you so much!!
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Re: John can build a wall in 30 days and Peter can demolish the same wall [#permalink]
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John can build a wall in 30 days and Peter can demolish the same wall in 40 days.

Let Rate of John = J and Rate of Peter = P
Rate * Time = Work = 1 (As Work is same for both of them)

J * 30 = 1
=> J = 1/30
This means that John can do 1/30th of the work in 1 day

P * 40 = 1
=> P = 1/40

When they work together on the same days then effective work rate = J - P as P is demolishing the wall
=> Effective Rate = J - P = 1/30 - 1/40 = 4/120 - 3/120 = 1/120
But they work on alternate days = >Rate = 1/2 * 1/120 = 1/240


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?

Now, wall will be built first when they have worked together for few days and then John works one more day to finish the work
Now, John can do 1/30th of the work in 1 day
=> They have to work together to finish 1 - 1/30 = 29/30 of the work

Now, when they work together on alternate days combined rate = 1/240

=> 1/240 * Time = 29/30
=> Time = 232 days

=> Total Time = Time they worked together to finish 29/30 of the work + Time taken by John to finish 1/30th of of the work = 232 + 1 = 233 days

So, Answer will be 233
Hope it helps!

Watch following video to MASTER Work Rate Problems

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