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

Question

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?

A. 232
B. 233
C. 234
D. 239
E. 240

A. 232
B. 233
C. 234
D. 239
E. 240

KarishmaB · Accepted Answer

John does (1/30)th of the work in a day. Let's find the number of days it takes to do (29/30)th of the work

John and Peter do 1/30 - 1/40 = 1/120 of the work in 2 days

So they do (29/30)th of the work in    * 2 = 232 days

John will do the last (1/30)th of the work in 1 day to give 233 days

Answer (B)

Henry S. Hudson Jr. · Answer

We need to assume John will work one more day since the question asks when the wall will FIRST be built.

The answer choices do not contain fractions either.

Let john work x +1 days. Let Peter work x days. John's rate is 1/30 of the wall per day. Peter's rate is -1/40 of the wall per day.

(x+1)/(30)-(x)/(40)=1

Solving for x we obtain 116. So Peter worked for 116 days and John worked for 117 days. 116+117=233 days.

Method 2:

Let the wall represent 120 units of work. Then John's rate is 4 units per day and Peter's is -3 units per day.

In two days 1 unit is completed. In 230 days, 115 units are completed.

In day 231 John produces 4 units so we have 119 units.

In day 232 Peter demolishes 3 units so we have 116 units.

In day 233 John produces 4 units so we have 120 units and have completed the job.

KanishkM · Answer

IMO E

LCM of 30 and 40 = 120

Rate of John = 4 unit /day

Rate of Peter = 3 unit/day (demolish will be -)
D1---D2----D3-----D4
4----(-3)-----4----(-3)

Work done will be 1 unit in 2 days
120 units will be done in 240 days

eswarchethu135 · Answer

Work done by John in 1 day =  \frac{1}{30}

Work done by Peter in 1 day =  \frac{-1}{40}

Work done by them in 2 days is  \frac{1}{30} - \frac{1}{40}  =  \frac{1}{120}

Work done in 1 day is  \frac{1}{240}

So it takes 240 days to build the wall for first time.

OPTION:  E

Archit3110 · Answer

rate of John = 1/30
rate of Peter = 1/40
combined rate = 1/30-1/40 = 1/120 ; 2 days work

John rate for rest of the days would be (29/30/ 1/120 ) * 2 = 232
since John has been working since day 1 ; 232+ 1; 233 days

stne · Answer

Hi  VeritasKarishma ,
Why do we have to assume that john will finish the work? Why can't peter finish the work?

Below is my analysis, please can you confirm if the same is correct or not?

I guess since Peter Demolishes then John would actually have to build a little bit more than the whole wall , for Peter to finish the wall.

So if Peter were to finish then , we would actually have built more than the whole wall, and the time taken would be 240 days.
But we are asked " When was the whole wall built for the first time" we have to let John Complete the wall. 
So in the last day John has to do 1/30 of the work.
Hence we have to find how much time Both John and Peter will take to do 29/30 of the work, leaving 1/30 work for John to finish up.

Hence total days is time taken by John and Peter to do 29/30 of the work plus one day that John will take to finish.

Is this analysis correct?

madhulis · Answer

As question asks, we need to find the number of days to build the wall first. This implies that we can not let the Peter demolish wall anymore after the wall is built. Hence, John will work for x+1 days and peter will work for x days.

Let the wall represent 120 units of work.
John's rate is 4 units per day 
Peter's is -3 units per day.

Combining the rates we get, 1 unit out of 120 units is completed in 2 days.

in x+1 days john can do 4(x+1) units of total work.

in x days peter can do 3x units of work. (negative work)

total work - combined work of peter and john = 0

let's put values in the equation, 
120-(4(x+1)-3x)=0
120-x-4=0
x=116.... (no of days taken by peter)

x+1=117.... (no of days john took to build)

hence, 116+117=233...total no days taken by john and peter to end up with a built wall.

Posted from my mobile device

rvgmat12 · Answer

Let the work be 120 units

John does 4 units per day and Peter does -3 units per day

Every two days = 1 unit added

232 days = 116 units added

233 days = 120 units added

hadimadi · Answer

Hi,

Work rate of John: 1/30
WR of Peter: -1/40
Days John works: x+1
Days Peter Works: x
John always works one more day because a) he starts, and b) the work will FIRST be done after John finishes it, and NEVER when Peter was the last one to work on it. This is because Peter always destroys parts of it, so it must first be finished after Peter.

-> 1=(1/30)(x+1)-(1/40)(x)
 -> x=116, x+1=117

Adding both you get (B)

BrushMyQuant · Answer

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 B 
Hope it helps!

Watch following video to MASTER Work Rate Problems

https://www.youtube.com/watch?v=dRxzi_x3ZwY

Wadree · Answer

John builds in 1 day = 1 / 30 = 4 / 120 of wall
Peter destroys in 1 day = 1 / 40 = 3 / 120 of wall
In 2 days .... Wall progress =   -   = 1 / 120 
So...it must take 240 days to finish da wall...right? ...NO..... here's why......
1 / 120 built in = 2 days .....
So.... 116 / 120 built in = 116 × 2 = 232 days......
But remember.....?...... John works every odd day....so john will work on 233rd day.....aaand...john builds in 1 day = 4 / 120

So...after 116 / 120 is built in 232 days.... John will build on 233rd day the rest 4 / 120 of wall...and finish.....so it'll be finished in 233 days.....

! nah id win!

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

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