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

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Manager
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This year Henry will save a certain amount of his income, [#permalink]

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New post 28 Jan 2007, 08:42
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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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Re: PS - Henry and fraction of his income [#permalink]

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New post 28 Jan 2007, 23:11
TOUGH GUY 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 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)


Income = X

Saving = Y

Spending = X-Y

Now,

Y( 1+ r) = (X-Y) /2

we have to calculate Y/X

After solving we get

Y/X= 1/ 3+2r
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New post 29 Jan 2007, 03:51
total income this year = t

amount spent this year = y
amount saved this year = x

Question translated. what is x / (x+ y) ?
=> What is 1 / (1 + Y/X) ? -----------------------1

amount available for spending next year = (amount saved this year) * (r+1) = x * (r+1)
But, amount available for spending next year = (amount spent this year) / 2 = y / 2
Thus, x*(r+1) = y/2

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

putting 2 in 1

1 / (1 + 2*(r + 1))

1/(3 + 2r) or E
  [#permalink] 29 Jan 2007, 03:51
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This year Henry will save a certain amount of his income,

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