A tree on first day grows 1/2 of its size second day 1/3 of its size on the previous day similarly than 1/4 and so on..U have calculate after how many days the tree will be 100 times of original size.

• 198 days
  
  suppose 'x' is initial size and 'n' is no. of days.
  
  1st day increment in size of tree = (1/2)x
  After 1st day , size of tree = x+(1/2)x= (3/2)x
  
  2nd day increment in size of tree = (1/3)*(3/2)x=(1/2)x
  After 2nd day , size of tree = (3/2)x+(1/2)x=2x
  
  3rd day increment in size of tree =(1/4)*2x=(1/2)x
  After 3rd day , size of tree = 2x+(1/2)=(5/2)x
  
  It is clear that every day tree grows (1/2)x in size.
  
  therefore , according to given condition
  
  x+ (1/2)x*n=100x
  n=198 days.
• 12 years agoHelpfull: Yes(80) No(0)
• @ASHUTOSH : In question it written on first day grows 1/2 of its size
  So,height of tree at end of day is 1.5x ,similarly,on second day 2x,and so on till 100x.It will form an AP with common diff. of 0.5x
  1.5x+2x+2.5x+.......+100x
  
  Tn=a+(n-1)d
  100x=1.5x+(n-1)0.5x
  n=>198
  so,it takes 198 days to grow tree 100 times the original.
• 11 years agoHelpfull: Yes(7) No(1)
• as pargat pal singh explained, it is true but need minor modification to achieve real answer is given below:
  t1=x, common difference=x/2 and tn=100x(This sequence is in A.P)
  so, tn=t1+(n-1)*d
  => 100x = x + (n-1) * x/2
  => 99x = (n-1) * x/2
  =>198 = n-1
  => n=199
  so answer is 199 days.
• 11 years agoHelpfull: Yes(6) No(8)
• in 198 days the tree will be 100 times of original size.
• 12 years agoHelpfull: Yes(2) No(5)
• 198 days
  
  well explained by Pargat Pal singh
• 12 years agoHelpfull: Yes(1) No(3)
• Assume intial size of tree is 100
  then next day size=100+100/2=150
  then nxt day size=150+1/3(150)=200 and so on
  so see the difference is 50
  Hense (100*100)/50=200-2(for initial 100 it taken 2 days)=198//
• 11 years agoHelpfull: Yes(1) No(0)