Problem Solving - 54

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) 1/2(r+2)
(C) 1/(3r+2)
(D) 1/(r+3)
(E) 1/(2r+3)


Answer: E

Let total income = x
Let saved = y
=> spent = x-y

Total dollars available that he can spend next year = y(1+r)

Given y(1+r) = (x-y)/2
=> y = x/(2r+3)

Fraction (y/x) = 1/(2r+3)

Hence E