A tree on first day grows 1/2 of its size second day 1/3rd of its size on the previous daysimilarly than 1/4th and so on.u have to calculate after how many days the tree will be 100 times of its original size.ans -198 days

Madhusmita_behera
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Sep 15th, 2006
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diwankar
Profile Answers by diwankar

Jan 24th, 2008

Let initially size of tree be 'x' , no. of days be 'n'.
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

We can see that every day tree grows (1/2)x in size.

therefore , according to given condition

x+ (1/2)x*n=100x (here 'x' is initial size and 'n' is no. of days.)

n=198 days.