33 men can do a job in 30 days. Of 44 men startd the job together and after every day of the work one person leaves .what is the minimum number of days required to complete the whole work

• 44 days
  
  1 man can complete the work in 33*30=990 days.
  As daily 1 person leaves, so the work completed daily is like 44*(1/990) + 43*(1/990) + 42*(1/990)+.....
  For complete work we have to find how many terms of the series 44*(1/990) + 43*(1/990) + 42*(1/990)+..... results into sum 1.
  => (1/990)(44+43+42+....) = 1
  => 44+43+42+.... = 990
  For an A.P. with sum 990, let number of terms be n, where first term a=44, difference d=-1, then
  Sn=(n/2)[2a + (n-1)*-1]
  => 990=(n/2)[2*44 + (n-1)*-1]
  Above equation satisfies for n=44, hence number of days required are 44.
• 6 years agoHelpfull: Yes(0) No(0)