Problem Solving

Q) This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
A. 1/r+2
B. 1/2r+2
C. 1/3r+2
D. 1/r+3
E. 1/2r+3

Pls help me out with the solution.

Let income is I dollars
he saves X dollars this year
next year he will have X(1+r) dollars

X(1+r)=(I-X)/2
X(1+r)=I/2-X/2
X+Xr+X/2=I/2
X(3/2+ r)=I/2
X/I= 1/2r+3

Answer E

The answer is E.

Let saving = x, total income = y
So, task is to find x/y?

Totals spending this year = y-x

Acco. to question >

x(1+r) = (y-x)/2

solve to get x/y.

Thank you guys the answer is E