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A sum of money is invested at simple interest, partly at 4% and remain

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A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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New post 27 Sep 2018, 04:37
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

81% (01:33) correct 19% (03:38) wrong based on 27 sessions

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A sum of money is invested at simple interest, partly at 4% and remaining at 7% annual rates of interest. After two years, the total interest obtained was $2100. If the total investment is $18000, what was the sum of money invested at 4% annual rate of interest?

(A) $5500
(B) $6000
(C) $7000
(D) $10500
(E) $11000

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Re: A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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New post 27 Sep 2018, 05:20
Bunuel wrote:
A sum of money is invested at simple interest, partly at 4% and remaining at 7% annual rates of interest. After two years, the total interest obtained was $2100. If the total investment is $18000, what was the sum of money invested at 4% annual rate of interest?

(A) $5500
(B) $6000
(C) $7000
(D) $10500
(E) $11000


Since it's a simple interest case so the interest for each year on each sum will remain constant

and 4% for 1 year = 8% for two years
and 7% for 1 year = 14% for two years

Let, SUm invested at 4% = x
i.e.e Sum invested at 7% = 18000-x

\((8/100)*x + (14/100)*(18000-x) = 2100\)

i.e. 8x+252000-14x = 210000

i.e. 6x = 42000

i.e. x = 7000

Answer: Option C
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Re: A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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New post 27 Sep 2018, 07:54
Given that the total interest in 2 years is 2,100. We can try picking from the answer choices.

Since total investment is 18,000 we pick investment for 4% to be 6,000

We try 6,000 * 4/100 = 240

12,000 * 7/100 = 840

If we add them we get 1,080 * 2 = 2,160 in 2 years making it larger than the desired interest.

From this we should be able to realize that we should increase the amount allotted for the 4%

And the answer would be C.

7,000 * 4/100 = 280

11,000 * 7/100 = 770

Added together we get 1,050 * 2 = 2,100

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Re: A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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New post 28 Sep 2018, 02:33
Bunuel wrote:
A sum of money is invested at simple interest, partly at 4% and remaining at 7% annual rates of interest. After two years, the total interest obtained was $2100. If the total investment is $18000, what was the sum of money invested at 4% annual rate of interest?

(A) $5500
(B) $6000
(C) $7000
(D) $10500
(E) $11000


So my approach was to calculate the rate of interest which gives 2100 as interest.

(18000 * 2 * x)/100 = 2100
rate comes out to be (35/6)

4 -------------------- 7
----------35/6--------
7/6------------------11/6

amount invested at 4% = (7/6) * (6/18) = (7/18)

so amount is 7000.
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Re: A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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New post 28 Sep 2018, 03:33
Hi,

It is a simple interest question, so there is no big calculations here.

We can eliminate the answer choices D and E.

Because given,

Total investment = 18000

And total interest earned = 2100.

For a moment, let’s assume the amount is equally distributed.

Then,

4% of 9000 + 7% of 9000 = 360 + 630 = 990 for one year.

Total amount for two years is 1980.

Which is less than the actual total interest(2100) given in the question.

So the amount distributed in 4% should be lesser than the amount invested in 7%.

Hence we can eliminate D and E.

Answer as to be either A, B and C.

Also the amount 1980 was not too far from 2100, then the best answer choice to try would be answer choice C.

So,

4% of 7000 + 7% of 11000 = 280 + 770 = 1050 for one year.

Total amount for two years is 2100.

Which matches the amount given in the question.

So the answer is C.

Hope it helps.
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Re: A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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New post 02 Oct 2018, 18:52
Bunuel wrote:
A sum of money is invested at simple interest, partly at 4% and remaining at 7% annual rates of interest. After two years, the total interest obtained was $2100. If the total investment is $18000, what was the sum of money invested at 4% annual rate of interest?

(A) $5500
(B) $6000
(C) $7000
(D) $10500
(E) $11000


We can let the amount of money invested at 4% interest = n. The amount invested at 7% is (18,000 - n). We can create the following equation:

2 x 0.04n + 2 x 0.07(18,000 - n) = 2,100

0.08n + 2,520 - 0.14n = 2,100

-0.06n = -420

n = 7,000

Answer: C
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Re: A sum of money is invested at simple interest, partly at 4% and remain &nbs [#permalink] 02 Oct 2018, 18:52
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