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

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
John can build a wall in 30 days and Peter can demolish the same wall  [#permalink]

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28 Jan 2019, 02:12
1
4
00:00

Difficulty:

(N/A)

Question Stats:

6% (00:55) correct 94% (01:57) wrong based on 36 sessions

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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?

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

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Location: India
Re: John can build a wall in 30 days and Peter can demolish the same wall  [#permalink]

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28 Jan 2019, 02:38
Bunuel 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?

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

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
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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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28 Jan 2019, 02:48
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
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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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28 Jan 2019, 02:54
1
Bunuel 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?

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

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 $$[\frac{(29/30)}{(1/120)}] * 2 = 232$$days

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

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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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28 Jan 2019, 04:30
1
Bunuel 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?

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

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
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Re: John can build a wall in 30 days and Peter can demolish the same wall   [#permalink] 28 Jan 2019, 04:30
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