a work is done by workers each day one worker get rmove and work get finished when all the workers remove.If they all together do the work then they take 0.6 of time taken by above procedure.find in how many days a single worker can complete a work

• Suppose single worker can complete the work in 'x' days
  
  Hence a workers one days work is 1/x
  
  Suppose there are 'n' workers
  
  Procedure 1---------
  The work would be completed in 'n-1' days (as given in question)
  
  Also,
  First days work is = n/x
  Second days work = (n-1) / x
  third days work = (n-2) / x
  n-1 days work is = 1/x
  
  Adding all days work
  
  n/x + n-1/x + n-2/x + 1/x = 1 { Standard equation }
  
  Solving, we get
  (1/x) * (n*(n+1)/2 ) =1
  
  Hence , x = n(n+1)/2 ----------Equation 1-------
  
  
  Procedure 2---------
  (1/x + 1/x + 1/x + .............1/x) * d = 1 { Standard equation }
  Total no of workers are 'n' and 'd' are the no of days , hence above equation becomes
  
  (n/x) * d = 1
  
  d = x/n days
  
  According to question
  Days in procedure 2 = .6 * days in procedure 1
  Hence,
  x/n = .6(n-1)
  
  x==6n(n-1) / 10 ----------------equation 2---------
  
  Solving equation 1 and 2..
  
  We get n = 11 , and x = 66 ..
  
  Hence Single worker complete works in 11 days ...(Ans)
  
• 9 years agoHelpfull: Yes(6) No(7)
• first procedure will complete in n days .
  second procedure will complete in x/n days
  according to question x/n=0.6n
  
  x=0.6n^2..................................eq1
  
  
  from given solution=n*(n+1)/2=x............................eq2
  solving 1 and 2
  n=5 and x =15days(answer)
  
• 9 years agoHelpfull: Yes(6) No(1)
• @Ajitesh Rai, work is completing in n days not in n-1 days
• 9 years agoHelpfull: Yes(1) No(1)
• anyone?? other than this
• 9 years agoHelpfull: Yes(0) No(0)
• is it's answer is 55 days
  
• 9 years agoHelpfull: Yes(0) No(0)
• Suppose, there are 'm' no. of total workers. In the first scenario, the work lasts for 'm' no. of days.
  
  w1+w2+w3+...+wm = W (total work)
  wi representing work on each day.
  
  m + m-1 + m-2 + ...... + 1 = W
  m(m+1)/2 = W ....eqn-1
  
  In second scenario,
  m*0.6m = W ....eqn-2
  
  Equating eqn-1 nd eqn-2
  m = 10.
  
  This means, in first scenario work was done in 10 days. So now in second scenario, this work will be done in 6 days.
  
  now the question boils down to- A work is done by 10 men in 6 days then how many days will be taken by 1 man to do the same work.
  
  1 * t = 10 * 6
  t = 60 days.
• 7 years agoHelpfull: Yes(0) No(1)