A $500 investment and a $1,500 investment have a combined yearly

SOLUTION

A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1 ,500 investment have?

(A) 9%
(B) 10%
(C) 10 5/8%
(D) 11%
(E) 12%

The ratio of investments is 500:1,500 = 1:3.

The deviation from the average return from $500 investment and $1,500 investment must be in the ration 3:1.

$500 investment return has the deviation from the mean of 8.5-7=1.5%, thus $1,500 investment return must have the deviation from the mean equal to 0.5%, which means that $1 ,500 investment has 8.5+0.5=9% yearly return.

Answer: A.
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Can be solved in 2 ways:

Fast method (Using ratios):

500$ & 1500 $ are in the ratio of 1:3

Since $500 gives a return on 7%, its 1.5 % away from 8.5%(the average return)

So ratio of returns of $500: $1500 should be in the ratio 3:1 deviation from 8.5%.

Therefore the return on $1500 = 8.5% + (1.5%/3) = 9%


Method 2 - General Math

Total annual return on both @ 8.5% = $170

Return on $500 @ 7% = $35.

So return on $1500 = $170-$35 = $135

Rate = (135/1500)*100 = 9%

(A) 9%

Total Capital = 2000

Total Return @ 8.5 % = 170

Return from 500 is @ 7% = 35

Balance = 170-35 = 135

Percentage = 100 * 135 / 1500 = 9

Option A.
8.5% on 2000=170
Of ths 7% of 500 is one part and x% of 1500 is the other part
7% of 500=35
170-35=135
x% of 1500=135
x=9

8.5 - 7 = 1.5
x - 8 = 0.5
x = 9

How 0.5? Because the ratio is 1:3. Check Image

Answer A
Time Taken 00:45
Difficulty level 600

A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1 ,500 investment have?

(A) 9%
(B) 10%
(C) 10 5/8%
(D) 11%
(E) 12%


Sol: Given that (1500+500)*(8.5%)= $170 Total return

and $500 has yearly return of 7% or 500*7/100 =$35...So remaining $135 is the return on Investment of $1500 so we have

1500*a/100=135 or a=135*100/1500 -----> a =9%

Ans is E

600 level is okay

Can someone elaborate this part please ?

It is given that the $500 investment is 1.5% BELOW the average. Which means that the $1500 investment has to be X% above average to balance the combined interest of 8.5%
500 * 1.5 = 1500 * X

X = (500 / 1500) * 1.5
X = (1/3) * 1.5 --> This can be re-written as X/1.5 = 1/3, which is the ratio that is mentioned above
X = 0.5% above the average
Ans = 9%

Hi Bunuel,

Could you please explain me the highlighted part
"The deviation from the average return from $500 investment and $1,500 investment must be in the ration 3:1.

$500 investment return has the deviation from the mean of 8.5-7=1.5%, thus $1,500 investment return must have the deviation from the mean equal to 0.5%, which means that $1 ,500 investment has 8.5+0.5=9% yearly return."

Though i understood the basic math approach, i am unable to understand in ratio approach.

Help is appreciated .
Thanks in advance ;

2000x0.85=0.7x500+15x
x=135/15=9%
A is the answer

Two amounts with two different weights and rates contribute to an overall rate of return on their combined amount

Straight weighted average
A = $500 portion
B = $1500 portion
r = interest rate

\((A_{r}*A_{amt})+(B_{r}*B_{amt}) = (A+B)_{r}* (A+B)_{amt}\)

\((.07)(500) +\\
(\frac{x}{100})(1500)= (.085)(2000)\)

\(35 + 15x = 170\)

\(15x = 135\)

\(x = \frac{135}{15} =\\
9\)

The interest rate for the $1,500 portion is 9 percent

Answer A
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Use weighted average formula:

\(\frac{w1}{w2}=\frac{Avg2 - Avg}{Avg - Avg1}\)

\(\frac{500}{1500}=\frac{x - 8.5}{8.5 - 7}\)

\(\frac{1}{3}=\frac{x - 8.5}{1.5}\)

\(1.5 = 3x-25.5\)

\(27 = 3x\)

\(9 = x\)

Let's calculate the yearly return for the $1,500 investment.

Given:
Total investment amount = $500 + $1,500 = $2,000
Combined yearly return on the two investments = 8.5% of the total investment

We know that the $500 investment has a yearly return of 7%.

Let's assume the yearly return for the $1,500 investment is represented by 'x'.

To find 'x', we can set up the following equation:

(7% of $500) + (x% of $1,500) = 8.5% of $2,000

(0.07 * $500) + (x% * $1,500) = 0.085 * $2,000

35 + (0.01x * $1,500) = 0.085 * $2,000

35 + 15x = 170

15x = 170 - 35 = 135

x = 135 / 15 = 9

Therefore, the $1,500 investment has a yearly return of 9%, which corresponds to option (A) in the given choices.