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A portion of $6600 is invested at a 5% annual return, while the remain

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ksharma12
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A portion of $6600 is invested at a 5% annual return, while the remain [#permalink] New post   15 Apr 2010, 16:50
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A portion of $6600 is invested at a 5% annual return, while the remainder is invested at a 3% annual return. If the annual income from the portion earning a 5% return is twice that of the other portion, what is the total income from the two investments after one year?

(A) $180
(B) $270
(C) $300
(D) $320
(E) $360
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B
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Re: A portion of $6600 is invested at a 5% annual return, while the remain [#permalink] New post   15 Apr 2010, 18:24
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ksharma12 wrote:
A portion of $6600 is invested at a 5% annual return, while the remainder is invested at a 3% annual return. If the annual income from the portion earning a 5% return is twice that of the other portion, what is the total income from the two investments after one year?

Explanation please?


5x + 3y = z (total)
x + y = 6600

5x= 2(3y)
5x - 6y = 0

x + y = 6600
5x -6y = 0

Subtract both equations and you get x = 3600 so y = 3000

3600*.05 = 180
3000*.03 = 90
z (total) = 270
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Re: A portion of $6600 is invested at a 5% annual return, while the remain [#permalink] New post   16 Apr 2010, 07:44
Let a = the amount at 3% interest

.05(6600 – a) = 2(.03)(a)
.05(6600 – a) = .06a
330 – 0.05a = .06a
330 = .11a
33000 = 11a
a = 3000

So
3000(0.03) + (6600-3000)(.05) =
90 + 180 = 270
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Re: A portion of $6600 is invested at a 5% annual return, while the remain [#permalink] New post   30 Oct 2016, 01:56
ksharma12 wrote:
A portion of $6600 is invested at a 5% annual return, while the remainder is invested at a 3% annual return. If the annual income from the portion earning a 5% return is twice that of the other portion, what is the total income from the two investments after one year?

(A) $180
(B) $270
(C) $300
(D) $320
(E) $360
Attachment:
Capture.PNG
Capture.PNG [ 2.89 KiB | Viewed 12657 times ]


Or, \(5x = 2*3(6600 - x )\)

Or, 5x = 6*6600 - 6x

Or, 11x = 6*6600

Or, x = 3600

So, Interest on 5% Interest = 5/100 * 3600 => 180
Interest on 3% Interest = 3/100*3000 = > 90

SO, Total Interest is Rs 270

Hence answer will be (B) 270
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Re: A portion of $6600 is invested at a 5% annual return, while the remain [#permalink] New post   06 Dec 2016, 18:51
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x+y=6600

0.05x=2c
0.03y=c

0.05x=0.06y
(6600-y)(0.05)=2y(0.03)
330-0.05y=0.06y
330=0.11y
y=3000 --> this means x must be equal to 3600 (i.e. x+y=6600)

3600(0.05)+3000(0.05) = 270

B.
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Re: A portion of $6600 is invested at a 5% annual return, while the remain [#permalink] New post   07 Dec 2016, 05:50
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ksharma12 wrote:
A portion of $6600 is invested at a 5% annual return, while the remainder is invested at a 3% annual return. If the annual income from the portion earning a 5% return is twice that of the other portion, what is the total income from the two investments after one year?

(A) $180
(B) $270
(C) $300
(D) $320
(E) $360


Annual income from the portion earning a 5% is twice that of the other portion. So interest would be same from 5% if the other potion were earning twice i.e. at 6%.
So the two principals must be in the ratio 6:5.
Principal at 5% = 6*600 = 3600
Interest at 5% = 5% of 3600 = 180
Principal at 3% = 5*600 = 3000
Interest at 3% = 3% of 3000 = 90

Total interest = 180 + 90 = 270

Answer (B)
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Re: A portion of $6600 is invested at a 5% annual return, while [#permalink] New post   06 Sep 2019, 13:55
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Re: A portion of $6600 is invested at a 5% annual return, while [#permalink]
06 Sep 2019, 13:55
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