Let Henry's income be $100.
Let Henry save $y
So Henry spends $(100 - y)

Next year, as stated- for every $1 Henry saves, he would have $(1 + r) available to spend.
So as he has $y saved this year, he would have $ y*(1+r) available to spend next year.

Now as stated,

next year the amount available to spend will be equal to half the amount that he spends this year

Thus, Amout available to spend next year = 0.5 * amt spent this year
=> y(1+r) = 0.5*(100-y)

Calculate for y
=> y = 100/(3+2r)

Required fraction is:
$Saved/$Earned
=> y/100
=> (100/(3+2r))/100
=> 1/(3+2r)
=> Option E