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Last year Luis invested x dollars for one year, half at 8 percent simp

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Last year Luis invested x dollars for one year, half at 8 percent simp [#permalink]

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Last year Luis invested x dollars for one year, half at 8 percent simple annual interest and the other half at 12 percent simple annual interest. Now he wants to reinvest the x dollars for one year in the same two types of investments, but the lower rate has decreased. If the higher rate is unchanged, what fraction of the x dollars must he reinvest at the 12 percent rate so that the total interest earned from the x dollars will be the same for both years ?

(1) The lower rate is now 6 percent.
(2) The total amount of interest earned from the two investments last year was $3,000.
[Reveal] Spoiler: OA

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Kudos [?]: 128566 [0], given: 12180

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Re: Last year Luis invested x dollars for one year, half at 8 percent simp [#permalink]

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New post 29 Aug 2017, 10:40
last year :
Total SI = x/2 * 8/100* 1 + x/2 * 12/100* 1 = 20x/200 = x/10 ---------------> equation 1

this year :
let p be invested at lower rate 'r' while x-p will be invested at 12%
Total SI = pr/100 + 12(x-p)/100 ---------------------------------------------------> equation 2

We have to find p to know the fraction of the x dollars invested at 12% and total interest earned remains the same.
A.) The lower rate is now 6 percent.
r = 6%
Equating eq 1 and 2 , we can find p easily-
equation 2 becomes => 6p/100 + 12(x-p)/100 => (6p+12x-12p)/100 => 12x-6p/100
12x-6p/100 = x/10
12x-6p = 10x
2x = 6p
x = 3p
therefore p = x/3 invested at 6% while 2x/3 will be invested at 12%
Sufficient

B.) Knowing total interest earned gives us the value of x but still 2 unknowns, p & r.
Not sufficient

Hence, A

Please point out in case I have made a mistake.

Thanks.
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Kudos [?]: 8 [0], given: 56

Re: Last year Luis invested x dollars for one year, half at 8 percent simp   [#permalink] 29 Aug 2017, 10:40
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Last year Luis invested x dollars for one year, half at 8 percent simp

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