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David used part of $100,000 to purchase a house. Of the remaining port

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David used part of $100,000 to purchase a house. Of the remaining port  [#permalink]

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New post 18 Jun 2019, 12:18
The other method would be using allegation

Let the remaining amount be x then ,

\(\frac{1}{3}\) x 4 % and \(\frac{2}{3}\)x 6 %

So average is\(\frac{16}{3}\)

so \(\frac{16}{3}\) % of x =320

x =6000

So Amount invested in house is 94,000
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Re: David used part of $100,000 to purchase a house. Of the remaining port  [#permalink]

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New post 22 Jun 2019, 05:13
Hello,

suppose the amount spent on the house is X$ and the amount remaining is Y$

1/3 of Y were invested at 4% which gives (0.33*0.04)Y =0.0132Y (you can calculate this manually by multiplying 33 by 4 and adding the decimals later)
2/3 of Y were invested at 4% which gives (0.66*0.06)Y=0.0396Y

Given that: total investment amount=320$

so 0.0132Y + 0.0396Y=320$

0.0528Y=320$

y=6000$ approx. in this question you dont need the exact amount you need an approximate amount, so you can divide 300/0.05 which is 6000$

now you deduct Y from the original amount which is 100000$

the answer is 94000$ which is B
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Re: David used part of $100,000 to purchase a house. Of the remaining port  [#permalink]

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New post 23 Jul 2019, 21:44
Let the amount left after investing in the house be x.

(4/300)*x + (12/300)*x=320

x=6000

100000-6000= 94000

Ans: B
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Re: David used part of $100,000 to purchase a house. Of the remaining port  [#permalink]

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New post 02 Aug 2019, 10:25
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nalinnair wrote:
David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?

(A) $96,000
(B) $94,000
(C) $88,000
(D) $75,000
(E) $40,000


Let h be the cost of the house, remaining money for investment --> (100,000-h)
(100,000-h)(1/3 * 4/100) + (100,000-h)(2/3 * 6/100) = 320
(100,000-h)(4/300 + 12/300) = 320
(100,000-h) = 320 * 300/16
100,000-h = 6,000
100,000 - 6,000 = h
h = 94,000
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Re: David used part of $100,000 to purchase a house. Of the remaining port  [#permalink]

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New post 04 Aug 2019, 05:42
Probus wrote:
The other method would be using allegation

Let the remaining amount be x then ,

\(\frac{1}{3}\) x 4 % and \(\frac{2}{3}\)x 6 %

So average is\(\frac{16}{3}\)

so \(\frac{16}{3}\) % of x =320

x =6000

So Amount invested in house is 94,000

Why do we only calculate *0.04 and not *1.04?
Because usually we calculate principle*(1+%rate)^1 correct?
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Re: David used part of $100,000 to purchase a house. Of the remaining port   [#permalink] 04 Aug 2019, 05:42

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