A is a creater nd B is a destroyer. A can complete a building in 20 days while B can destroy it in 30 days. If both working alternate days,then after how much time will be the building completes for the first time?

• Ans)115 days
  
  A 1 day=+1/20
  B 1 day=-1/30
  In 2 days building will be complete 1/20-1/30=1/60
  so days are reqired=120...but
  If full building work is 1, then before B destroy ,A complete the building .so
  completed building work before A finished =>(1-1/20)=19/20 ,this will gives the number of pair A,B works...
  consider x is number of pair days work of A,B...
  
  1/60*x=19/20=>x=57;
  so number of days=2 * pair days ;
  number of days A and B work =114;
  at last A done ramaining work, so 114+1=115
  Ans)115 days
  
  
• 11 years agoHelpfull: Yes(57) No(3)
• 115
  
  A's 1 day=+1/20
  B's 1 day=-1/30
  In 2 days building will be complete 1/20-1/30=1/60
  
  (1-1/20 = ) 19/20 part of wall will be made in 114 days.
  on 115th day balance 1/20 th will be made by creator.
  
• 11 years agoHelpfull: Yes(30) No(4)
• Let us say that the wall is of 60 bricks
  
  A builds 3 bricks every day
  B destroys 2 bricks every day
  
  If A and B work on alternate days then 1 brick will be added every 2 days.
  
  After 114 days, 57 bricks will be added. Now it will be turn of A to build 3 bricks. Hence on 115th day 60 bricks will be completed
• 10 years agoHelpfull: Yes(19) No(0)
• A's 1 day=+1/20
  B's 1 day=-1/30
  In 2 days building will be complete 1/20-1/30=1/60
  2 days =1/60
  =>2*60 days=1
  i.e it require 120 days....
• 11 years agoHelpfull: Yes(10) No(33)
• in 2 days they complete building 1/60 part.so they both complete in 120 days
• 11 years agoHelpfull: Yes(4) No(19)
• one day creation of the A is =1/20
  one day destruction of the B is =1/30
  so 2 day construction is=1/20-1/30=1/60
  to complete work each take 60 turn
  so days are reqired=120
• 11 years agoHelpfull: Yes(4) No(18)
• a does 1/20 work in 1 day
  b destroys 1/30 work in 1 day.
  together they do 1/20-1/30 work in one day that is 1/60 work
  hence they take 60 days to complete building
• 11 years agoHelpfull: Yes(3) No(23)
• Lets say total work to be done is LCM of 20&30 which is 60 UNIT.
  
  A's work for 1 day is 60/20=3 UNIT.
  
  B's work for one day is 60/30=2 UNIT but negative or -2 unit.
  
  now here A starts first because B demolishes , or demolition only can be done if there is some work already done.
  so here (A+B) will be a pair for two days work which yields 1 unit work in 2 days.
  hence this will continue for 114 days which will yield 57 unit work but on the end of 115th day the works will be 60 unit or 100% hence the work will be first completed on 115th day.
  
  
  HENCE answer is 115 day
  
  
  
  
  
  
  
  
  
  
• 8 years agoHelpfull: Yes(3) No(0)
• can anyone explain why the solution shouldn't stop at 120 days?
• 11 years agoHelpfull: Yes(0) No(4)
• Days Efficiency
  A - 20(days) ----- 5% (100/20)
  B - 30(days) ----- -3.33% (100/30)
  
  Total efficiency in 2 days = 1.66
  
  Building will be completed when eff =100;
  
  ( 100 / 1.66 )*2 = 120 days
• 11 years agoHelpfull: Yes(0) No(5)
• correct answer=120
  short cut method:
  days total unit
  60
  a=20 3
  b=30 - 2
  total one day work=1
  here a start the work so pattern like ab ab ab......
  so one pattern work=60
  so 60/1=60 pattern
  one pattern =2 days
  so 60 pattern 2*60=120 days is the correct answer
  
  total work 12
  
• 8 years agoHelpfull: Yes(0) No(2)
• A one days work 1/20= 5%
  B one day work 1/30 = -3.33%
  
  2 day's work = 5-3.33= 1.68%
  
  They work together until they complete the 95% work and final 5% would be done by A itself
  
  1.68*x=95
  x=114
  now A will do the remaining 5% of work in last day it would be = 114+1= 115
• 7 years agoHelpfull: Yes(0) No(0)
• let total unit of work is 60 unit
  then A do 3 nit of work in 1 day and B do 2 unit of work in 1 day
  resultant nit of work = 3-2=1 unit per day
  it takes 57 days to complete 57 unit of work...... as next day A do 3 unit of work and it reaches 60 unit(total work)
  hence total 57+1= 58 days required to complete the building for the first time :P
• 7 years agoHelpfull: Yes(0) No(0)