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19 Feb 2018, 23:24
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Difficulty:

45% (medium)

Question Stats:

69% (02:05) correct 31% (02:13) wrong based on 58 sessions

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Mr. Williams invested a total of $12,000 for a one-year period. Part of the money was invested at 5% simple interest, and the rest was invested at 12% simple interest. If he earned a total of$880 in interest for the year, how much of the money was invested at 12%?

(A) $1,920 (B)$4,000

(C) $4,800 (D)$7,200

(E) $8,000 _________________ Senior Manager Joined: 31 May 2017 Posts: 348 Re: Mr. Williams invested a total of$12,000 for a one-year period. Part  [#permalink]

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19 Feb 2018, 23:41
1
We can solve this question quickly by plugging in values and eliminating wrong answers straight away.

Step 1: Total interest rate accumulated is $880. Lets take a random split say$6000 each. Now if you calculate $6000 at 12% interest is$720 and at 5% is 300 which gives us $920. So part of amount invested at less than 12% is definitely less than$6000. Eliminate Option D and E. Actually we can eliminate option A without much calculation as well.

So we are left with option B and C.

Step 2:
Next lets take next highest value , $4800 ,which at 12% will yield$576 and rest of $7200 at 5% will yield 360.$576+$360 >$880.

So we are left with option B - $4000 - which @12% gives 480 and balance$8000 at 5% gives 400 - $480 +$400 = $880. Ans: B _________________ Please give kudos if it helps Resources | | | | | Senior SC Moderator Joined: 22 May 2016 Posts: 3077 Mr. Williams invested a total of$12,000 for a one-year period. Part  [#permalink]

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24 Feb 2018, 01:12
1
1
Bunuel wrote:
Mr. Williams invested a total of $12,000 for a one-year period. Part of the money was invested at 5% simple interest, and the rest was invested at 12% simple interest. If he earned a total of$880 in interest for the year, how much of the money was invested at 12%?

(A) $1,920 (B)$4,000

(C) $4,800 (D)$7,200

(E) $8,000 Try a weighted average approach, similar to that in mixture problems. Interest, as a percent, is like concentration. Let x = amount in dollars invested at 5% (below, equivalent to "weight") Let y = amount in dollars invested at 12% (below, equivalent to "weight") $$x + y = 12,000$$ $$x = 12,000 - y$$ $$(Rate_1)(Weight_1) + (R_2)(W_2)$$ = Total Interest $$.05x + .12y = 880$$ Substitute $$x = (12,000 - y)$$ $$.05(12,000 - y) + .12y = 880$$ $$600 - .05y + .12y = 880$$ $$.07y = 280$$ $$y = \frac{280}{.07}=\frac{28,000}{7}=4,000$$ Answer B _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver Mr. Williams invested a total of$12,000 for a one-year period. Part   [#permalink] 24 Feb 2018, 01:12
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