Amith starts to work on the first day. On the second day two more friends join him. On the third day 3 more friends join him and so on they complete work in 30 days. The find the number of days 16 girls can finish the work completely given that a girl can work twice as fast as Amith and his friends

• 155 days.
  
  Let Amith or his friend alone can complete the work in 'x' days, then
  1 day work of Amith=1 day work of his friend=1/x
  Their 30 day's work=1/x + 3/x + 6/x + 10/x .... =1
  => 1/x (1 + 3 + 6 + 10 +....upto 30 terms)=1
  Sequence 1,3,6,10,15,... is called triangle number series with sum=n(n+1)(n+2)/6
  => (1/x) (30*31*32/2) =1
  => 1/x=1/4960
  As girl is of twice capacity of a boy, so 1 girl's 1 day work = 2*(1/x)=2*1/4960=1/2480
  So 16 girl's 1 day work=16*(1/2480)=1/155
  Hence required days=155
• 7 years agoHelpfull: Yes(2) No(10)