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Word Problem - Henry's income

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Resurgent: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Aug 23, 2009 8:09 am; Thanked: 1 times

by Resurgent » Thu Oct 22, 2009 12:34 am

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)

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Source: Beat The GMAT — Problem Solving | Thu Oct 22, 2009 12:34 am

xcusemeplz2009: Master | Next Rank: 500 Posts; Posts: 399; Joined: Wed Apr 15, 2009 3:48 am; Location: india; Thanked: 39 times

by xcusemeplz2009 » Thu Oct 22, 2009 12:51 am

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

It does not matter how many times you get knocked down , but how many times you get up

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Thu Oct 22, 2009 1:44 am

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

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xcusemeplz2009: Master | Next Rank: 500 Posts; Posts: 399; Joined: Wed Apr 15, 2009 3:48 am; Location: india; Thanked: 39 times

by xcusemeplz2009 » Thu Oct 22, 2009 1:48 am

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

It does not matter how many times you get knocked down , but how many times you get up

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uttam.albela: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Fri Aug 28, 2009 2:40 am; Location: Singapore; Thanked: 11 times

by uttam.albela » Thu Oct 22, 2009 1:59 am

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

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Resurgent: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Aug 23, 2009 8:09 am; Thanked: 1 times

by Resurgent » Mon Nov 02, 2009 11:04 pm

The OA is E

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