Henry's spending

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saurabhmahajan: Master | Next Rank: 500 Posts; Posts: 250; Joined: Thu Jan 07, 2010 2:21 am; Thanked: 10 times

by saurabhmahajan » Tue Aug 10, 2010 11:58 pm

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 has 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

Thanks and regards,
Saurabh Mahajan

I can understand you not winning,but i will not forgive you for not trying.

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Source: Beat The GMAT — Problem Solving | Tue Aug 10, 2010 11:58 pm

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Wed Aug 11, 2010 12:19 am

saurabhmahajan wrote: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 has 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

Let the Income of Henry be X
Let the income Henry saves be S dollars
Therefore Henry will have S(1+r) dollars to spend next year.
Fraction to save = S/X
Now,
S(1+r) = (X-S)/2
2S(1+r) = (X-S)
X = 3S+2rS

Therefore S/X = S/S(3+2r)
= 1/(3+2r)

Hope this helps!!

"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

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likithae: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Thu Aug 05, 2010 2:39 am

by likithae » Wed Aug 11, 2010 1:12 am

kvcpk wrote:
saurabhmahajan wrote: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 has 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
Let the Income of Henry be X
Let the income Henry saves be S dollars
Therefore Henry will have S(1+r) dollars to spend next year.
Fraction to save = S/X
Now,
S(1+r) = (X-S)/2
2S(1+r) = (X-S)
X = 3S+2rS

Therefore S/X = S/S(3+2r)
= 1/(3+2r)

Hope this helps!!

thanks, but explain me in different approach.........

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