Problem Solving

Qn : When a certain tree was first planted, it was 4 feet tall, and height of the tree increased by constant amount each year for next 6 yrs. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of tree increase each year ?

a. 3/10
b. 2/5
c. 1/2
d. 2/3
e. 6/5

Suppose the tree's height increases by x units every year
Then at the end of the 4th year the height of the tree would be 4+4x and at the end of the 6th year the height of the tree would be 4=6x

Now using the second condition

Height after 4 years / height after 6 years = 5/6

So
(4+4x)/(4+6x) = 5/6

Solving this, x= 2/3

Whats the OA?

Thanks

that's correct...

thanks !!

Let the increase be x

Therefore acc to the qquestion,

4+6x=(4+4x)+1/5(4+4x)
=> 4+6x=5(4+4x)+(4+4x) ( By taking LCM)

5(4+6x)=5(4+4x)=(4+4x) (Cross Multiply)
30x+20= 24x+24
6x-4=0
6x=4
x=2/3