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# This year Henry will save a certain amount of his income,

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Manager
Joined: 08 Oct 2005
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This year Henry will save a certain amount of his income, [#permalink]  05 Aug 2006, 07:19
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. r / r+3

E. 1 / 2r+3
Senior Manager
Joined: 22 May 2006
Posts: 375
Location: Rancho Palos Verdes
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Re: Henry [#permalink]  05 Aug 2006, 10:27
Let saving amount = S and Income = I
S/I = ?

Spending = I - S
Available fund to spend = S*(1+r)
Spending/2 = S*(1+r)
(I-S)/2 = S*(1+r)
I-S = 2S(1+r)
I = S[2+2r+1]
S/I = 1 / 2r+3

Hence, E.
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Manager
Joined: 20 Mar 2006
Posts: 200
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Re: Henry [#permalink]  05 Aug 2006, 10:50
---------------This year--------------Next Year
Income------100(assume)---------- 0(given)
Save--------- x\$(assume)----------No info
spend--------100-x --------------- x(1+r) given

Also given in Q.stem --> x(1+r) = (100-x)/2
i.e x+xr = 50 - x/2
i.e x+x/2+xr = 50
3x/2+xr = 50
x(r+3/2) = 50
x= 50/(r+3/2)
x = 100/(2r+3)
Therfore he has to save 1/(2r+3) of income this year

Hence E
Manager
Joined: 08 Oct 2005
Posts: 101
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Re: Henry [#permalink]  05 Aug 2006, 20:04
freetheking wrote:
Let saving amount = S and Income = I
S/I = ?

Spending = I - S
Available fund to spend = S*(1+r)
Spending/2 = S*(1+r)
(I-S)/2 = S*(1+r)
I-S = 2S(1+r)
I = S[2+2r+1]
S/I = 1 / 2r+3

Hence, E.

OA is E good job buddy
Re: Henry   [#permalink] 05 Aug 2006, 20:04
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# This year Henry will save a certain amount of his income,

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