Problem Solving

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?

1.1/r+2
2. 1/2r+2
3. 1/3r+2
4. 1/r+3
5. 1/2r+3

Lets us say he has an income x

and he saves z fraction of it, thus saving is (zx)

so saving would be x-zx=x(1-z)

now amount available for spending next year would be (1+r)zx.

this amount should be half of this years spending thus equating the two we get

0.5x(1-z)=zx(1+r)

we need to solve for z(i.e. express in terms of r)

thus we wud get z=1/(3+2r)

thus answer is E.