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?

A. 1/(r+2)
B. 1(2r+2)
C. 1/(3r+2)
D. 1/(r+3)
E. 1/(2r+3)

IMO E

let i be the income ans s be the saving

s(1+r)=1/2*(i-s);(i-s) is the spending
solving s=i/(3+2r)

i.e 1/(3+2r) fraction of income

OA pls

xcusemeplz2009 wrote: (1+r)=1/2*(i-s);(i-s) is the spending
solving s=i/(3+2r)

Can you show how you are solving for s? Somehow i'm not able to get it

papgust wrote:

xcusemeplz2009 wrote: (1+r)=1/2*(i-s);(i-s) is the spending
solving s=i/(3+2r)

Can you show how you are solving for s? Somehow i'm not able to get it

my approach is
s*(1+r)=1/2*(i-s)
s+sr=1/2*(i-s)
2s+2sr=i-s
3s+2sr=i
s(3+2r)=i
s=i/(3+2r)=>s is 1/(3+2r) fraction of i

HTH

Assume salary this year = x
Saving this year = s
Expenditure this year = x-s

Expenditure next year = s*(1+r)
(Since 1 saving last year = 1+r expenditure this year
s saving last year= s*(1+r) expenditure this year)

Now what we have to find: saving last year / salary last year
s/x = ?

Given:

s*(1+r) = (x-s)/2
2s*(1+r)= x-s
2s+2sr=x-s
3s+2sr=x
s(3+2r)=x
s/x=1/(3+2r) Answer

let me know if this is not clear to you

The OA is E