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An investor receives a total combined return of 7% on his two differen

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An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 14 Jun 2016, 02:41
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An investor receives a total combined return of 7% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?

A. 7.25%
B. 7.5%
C. 8%
D. 8.5%
E. 9%

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Re: An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 14 Jun 2016, 04:30
Ans : B => 7.5%

7 % of 30000 = 6 % of 10000 + x % of 20000
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Re: An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 14 Jun 2016, 05:31
total investment = $30000
on which he receives 7% = 2100
now,
on his $10000 he receives 6% = $600
remaining $1500
which is (1500/20000)*100 = 7.5
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Re: An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 14 Jun 2016, 07:19
0.06 * 10000 + 20000x = 0.07(30000)
solving for x give x = 7.5%
option B
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Re: An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 06 Aug 2017, 21:53
1
Another quick short at this question will be:
What number can we multiply by 2 that when added to 6% and averaged we will get 7%? (Given that $20,000 is twice $10,000)
i.e. let x be that number,
So, (6% + (2x)%)/3 = 7
Hence, 6% + (2x)% = 21
Then (2x)% = 21-6 = 15
x = (15/2)% = 7.5%
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An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 07 Aug 2017, 15:03
Bunuel wrote:
An investor receives a total combined return of 7% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?

A. 7.25%
B. 7.5%
C. 8%
D. 8.5%
E. 9%

Take two zeros off the amounts for easier arithmetic. The weighted terms remain the same, proportionally.

Sometimes split interest problems can be treated as mixture problems. Two quantities at two different interest rates equal an overall or "average" interest rate of 7% on the two investments, summed.

6 percent return on 100
x percent return on 200
7 percent return on total, which is 100 + 200 = 300

.06(100) + \(\frac{x}{100}\)(200) = .07(300)

6 + \(\frac{200x}{100}\) = 21

6 + 2x = 21
2x = 15
x = 7.5 (percent, accounted for in \(\frac{x}{100}\))

Answer B
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Re: An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 07 Aug 2017, 21:03
Total return on investment is 7%, for investment - 30000$, which is 2100$.

Since he makes 6%(600$) from the initial investment of 10000$,
he would have to make 1500$ from the other 20000$ invested.

\(\frac{1500}{20000}*100\) = 7.5%
Since we have been asked to find the return on his investment, the percentage would be 7.5%(Option B)
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Re: An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 07 Aug 2017, 22:23
Bunuel wrote:
An investor receives a total combined return of 7% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?

A. 7.25%
B. 7.5%
C. 8%
D. 8.5%
E. 9%


Let the amount 20000 be invested at x% return.

So, Total interest received = 6/100* 10000 x/100 * 20000 = 200x + 600

Total investment = 30000

Total interest received = 7/100 * 30000 = 2100

-> 2100 = 200x +600
-> x = 7.5%

Answer B

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Re: An investor receives a total combined return of 7% on his two differen [#permalink]

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New post 10 Aug 2017, 10:42
Bunuel wrote:
An investor receives a total combined return of 7% on his two different investments. On his $10,000 investment he receives a return of 6%. What is the return on his $20,000 investment?

A. 7.25%
B. 7.5%
C. 8%
D. 8.5%
E. 9%


We let the return of his $20,000 investment be p percent and create the following equation:

(6/100)(10,000) + (p/100)(20,000) = (7/100)(10,000 + 20,000)

600 + 200p = 2,100

200p = 1,500

p = 7.5

Answer: B
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Re: An investor receives a total combined return of 7% on his two differen   [#permalink] 10 Aug 2017, 10:42
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