Question

p alone can build a wall in 10 days, Q alone can build the same wall in 20 days, and r alone can destroy the fully built wall in 8 days. The three of them work alone on the wall on successive days starting with p working on first day, Q on secend day and r on third day and the cycle then repeats. In how many days will the wall be built for the first time
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Answer 1

The work in three days = (1/10)+(1/20)-(1/8)=1/40..

Most of us will go wrong in taking 40*3=120 as the answer. That will be the time when the one wall will always be there. But there will be many times when the wall gets completed but some part gets broken by C

Now, our answer will never be a multiple of 3, since the work would complete before C comes into action..

Now in one day C breaks 1/8 wall, so we look for the work less this ..1-(1/8)=7/8 = 35/40

35/40 : 34/40 will be done by 34 days of all three.. next day it will be 1/10, so 34/40+1/10=38/40..

Next day it will be 1/20, so 38/40+(1/20)=40/40=1

So our answer is 35 days of A and B and 34 days of C = 35+35+34=104..

B..

Another way is to check choices..

1.102... Divide by 3..102=3*34, so 34 days of all three =34*(1/40)=34/40...NO

2. 104...104=3*34+2, so 34*(1/40)+(1/10)+(1/20)=1... YES