A and B are working on a job.A is the builder and B is the demolition man.A takes 20 days to construct a wall completely.B takes 40 days to demolish it completely.How much time do they take to build the wall completely if they work alternatively.If A starts the work

• A builds 1/20 th wall in one day
  B destroys 1/40 th wall in one day
  
  => In two days, (1/20) - (1/40) = (1/40)th wall is built
  => Average wall built in one day = 1/80
  
  => In 78 days , (78/80) th wall is built
  On 79th day, a takes 1/2 day to build remaining 2/80 th wall
  
  => Total time taken = 78.5 days
• 12 years agoHelpfull: Yes(8) No(5)
• Total work = LCM(20,40)=40 units
  For A
  20 days works = 40 units
  1 day works = 40/20=2 units
  For B
  40 days work = 40 units
  1 day work = 40/40 = 1 unit
  If A start the work and they do alternately.
  in First 2 day (work done by A and B) = 2-1= 1 unit
  2*38=76 days = 1*38 = 38 units work
  76 days + 1 day(last day A works)= 38 units+ 2 units
  total 77 days = 40 units work(which is total work)
  the Total time Taken = 77 Days
• 12 years agoHelpfull: Yes(4) No(0)
• as they do only 1/20-1/40 work in two days=1/40
  they take 76 days to complete 38/40
  on 77th day= 38/40+1/20=1
  so 77 days
• 11 years agoHelpfull: Yes(1) No(0)
• Ans 79
  On day 1 A will build 1/20 of the wall
  On Day 2 B will break 1/40th of it. Thus at the end of each 2 day period 1/40th of the wall will be built.
  Hence on the 78th day 39/40th of the wall will be built.
  On the 79th Day A will complete the wall fully
  
  
• 9 years agoHelpfull: Yes(0) No(0)