Certain no. of workers started working on a project. after each day one worker is reduced. Work completed when last worker left. In how many days one worker will finish the same work.

• Same as utkarsh jain ,but with more explanation.
  let each worker does 1 unit of work each day
  if there are x workers then work done on first day =x
  next day work done= x-1
  .
  .
  
  like wise work done on last day=1 unit
  total work done in all=1+2+3+....+x=x(x+1)/2
  
  example ,let there are 5 workers on the 1st day of project.
  and each worker works for 6 hours a day.
  no. of workers total work time
  5 30
  4 24
  3 18
  2 12
  1 6
  
  total hours worked= 30+24+18+12+6=90
  
  if there is only one worker then it would require 90/6=15 days to finish the work.
  
  
  and from the formula given by utkarsh =(5*6)/2=15 days.
• 10 years agoHelpfull: Yes(29) No(1)
• let each worker does 1 unit of work each day
  if there are x workers then work done on first day =x
  next day work done= x-1
  .
  .
  
  like wise work done on last day=1 unit
  total work done in all=1+2+3+....+x=x(x+1)/2
  hence proved.
• 10 years agoHelpfull: Yes(15) No(2)
• No of days = no of workers =x
  So 1 man will complete the work in x^2 days
• 10 years agoHelpfull: Yes(0) No(18)
• let there be x workers and 1 worker do w work in one day
  total work(with one worker reduced every day)
  wx+w(x-1)+w(x-2).........+w*1=w(x+x-1.....x-n) (x-n=1)
  =w[x+x+x ...xtimes -(1+2+3....+x-1 )=x^2-{(x-1)*x/2}]
  w*x*(x+1)/2
  which is total work hence one worker will have to work x*(x+1) days
• 9 years agoHelpfull: Yes(0) No(2)