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

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Senior Manager
Joined: 08 Jun 2004
Posts: 498
Location: Europe
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Kudos [?]: 24 [0], given: 0

This year Henry will save a certain amount of his income, [#permalink]  29 Apr 2006, 21:03
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(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
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)
Manager
Joined: 23 Mar 2006
Posts: 75
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Kudos [?]: 1 [0], given: 0

I dunno how to do this one. Whoever cracks it, please explain it.
VP
Joined: 28 Mar 2006
Posts: 1383
Followers: 2

Kudos [?]: 20 [0], given: 0

It looks like D.....

I will explain if D is correct...Thanks ...
VP
Joined: 21 Sep 2003
Posts: 1065
Location: USA
Followers: 3

Kudos [?]: 40 [0], given: 0

Should be E.

x = This year's income
y = this year's spending
x-y = this year's saving

Next year's amount avaulable for spending = (x-y)(1+r)
Required (x-y)/x ?

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

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

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

Hence (x-y)/x = 1/(2r+3)
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- Bernard Edmonds

VP
Joined: 28 Mar 2006
Posts: 1383
Followers: 2

Kudos [?]: 20 [0], given: 0

giddi77 wrote:
Should be E.

x = This year's income
y = this year's spending
x-y = this year's saving

Next year's amount avaulable for spending = (x-y)(1+r)
Required (x-y)/x ?

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

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

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

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

Good solution with a lot of clarity.....Thanks!!
Manager
Joined: 23 Mar 2006
Posts: 75
Followers: 1

Kudos [?]: 1 [0], given: 0

Thanks Giddi,

I don't think this would have struck me had I seen it on the test
Senior Manager
Joined: 08 Jun 2004
Posts: 498
Location: Europe
Followers: 1

Kudos [?]: 24 [0], given: 0

OA is 'E'.

Perfect Giddi.
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