Latest HCL Aptitude Question SOLUTION: 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 tim

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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.

Asked In HCL jyothi (12 years ago)

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Pargat Pal Singh  (12 years ago)

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.

Is this solution Helpfull? Yes (80) | No   

ROHIT GUPTA  (11 years ago)

@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.

Is this solution Helpfull? Yes (7) | No (1)  

Ashutosh Ranjan  (11 years ago)

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.

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Sukham  (12 years ago)

in 198 days the tree will be 100 times of original size.

Is this solution Helpfull? Yes (2) | No (5)  

Mahesh  (12 years ago)

198 days

well explained by Pargat Pal singh

Is this solution Helpfull? Yes (1) | No (3)  

santosh  (11 years ago)

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//

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