A $200 investment at x percent per annum and a $500 investment at y percent per annum have a combined yearly return of 10 percent of the total of the two investments. If $400 is invested at x percent and $600 is invested at y percent per annum to give a combined yearly return of 9.2 percent of the total of the two investments, what will be the combined percentage yearly return of the total investment if $100 each is invested at x percent per annum and y percent per annum respectively?a)5%b)7.5%c)8.5%d)10%e)17%Correct answer is option 'C'. Can you explain this answer?

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A $200 investment at x percent per annum and a $500 investment at y percent per annum have a combined yearly return of 10 percent of the total of the two investments. If $400 is invested at x percent and $600 is invested at y percent per annum to give a combined yearly return of 9.2 percent of the total of the two investments, what will be the combined percentage yearly return of the total investment if $100 each is invested at x percent per annum and y percent per annum respectively?

a)
5%
b)
7.5%
c)
8.5%
d)
10%
e)
17%

Correct answer is option 'C'. Can you explain this answer?

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A $200 investment at x percent per annum and a $500 investment at y pe...

Given:

Case-I
- Principal , P = $200
  - Rate of interest = x% p.a.
- Principal, P = $500
  - Rate of Interest = y% p.a.
- Combined yearly return = 10%
Case-II
- Principal, P = $400
  - Rate of interest = x% p.a.
- Principal, P = $600
  - Rate of Interest = y% p.a.
- Combined yearly return = 9.2%

To Find: Combined yearly return if $100 each is invested at x% p.a. and y% p.a.?

Let the combined yearly return be R%
So, Return on $200 invested at R% p.a. = Return on $100 at x% p.a. + Return on $100 at y% p.a.

Approach:

For finding the value of R, we need to find the value of x and y.
We are given two cases in which the principals are invested at x% and y% per annum and we are also given the combined yearly return for both the cases
- The combined yearly return is equal to the sum of the returns of the individual investments
- Writing the combined yearly return equations for each of the case will give us an equation in x and y
We will solve both the equations to get the value of x and y, which will be used to calculate the yearly return on $100 each invested at x% and y% p.a.

Working out:

Case-I

As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation
2x +5y = 70……………..(1)

2. Case-II

As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation

3. Solving (1) and (2), we have y = 12 and x = 5
4. Hence, combined yearly return on investment of $100 each at x% and y% can be calculated as

Answer : C

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Most Upvoted Answer

A $200 investment at x percent per annum and a $500 investment at y pe...

Given:

Case-I
- Principal , P = $200
  - Rate of interest = x% p.a.
- Principal, P = $500
  - Rate of Interest = y% p.a.
- Combined yearly return = 10%
Case-II
- Principal, P = $400
  - Rate of interest = x% p.a.
- Principal, P = $600
  - Rate of Interest = y% p.a.
- Combined yearly return = 9.2%

To Find: Combined yearly return if $100 each is invested at x% p.a. and y% p.a.?

Let the combined yearly return be R%
So, Return on $200 invested at R% p.a. = Return on $100 at x% p.a. + Return on $100 at y% p.a.

Approach:

For finding the value of R, we need to find the value of x and y.
We are given two cases in which the principals are invested at x% and y% per annum and we are also given the combined yearly return for both the cases
- The combined yearly return is equal to the sum of the returns of the individual investments
- Writing the combined yearly return equations for each of the case will give us an equation in x and y
We will solve both the equations to get the value of x and y, which will be used to calculate the yearly return on $100 each invested at x% and y% p.a.

Working out:

Case-I

As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation
2x +5y = 70……………..(1)

2. Case-II

As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation

3. Solving (1) and (2), we have y = 12 and x = 5
4. Hence, combined yearly return on investment of $100 each at x% and y% can be calculated as

Answer : C

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Community Answer

A $200 investment at x percent per annum and a $500 investment at y pe...

Given:

Case-I
- Principal , P = $200
  - Rate of interest = x% p.a.
- Principal, P = $500
  - Rate of Interest = y% p.a.
- Combined yearly return = 10%
Case-II
- Principal, P = $400
  - Rate of interest = x% p.a.
- Principal, P = $600
  - Rate of Interest = y% p.a.
- Combined yearly return = 9.2%

To Find: Combined yearly return if $100 each is invested at x% p.a. and y% p.a.?

Let the combined yearly return be R%
So, Return on $200 invested at R% p.a. = Return on $100 at x% p.a. + Return on $100 at y% p.a.

Approach:

For finding the value of R, we need to find the value of x and y.
We are given two cases in which the principals are invested at x% and y% per annum and we are also given the combined yearly return for both the cases
- The combined yearly return is equal to the sum of the returns of the individual investments
- Writing the combined yearly return equations for each of the case will give us an equation in x and y
We will solve both the equations to get the value of x and y, which will be used to calculate the yearly return on $100 each invested at x% and y% p.a.

Working out:

Case-I

As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation
2x +5y = 70……………..(1)

2. Case-II

As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation

3. Solving (1) and (2), we have y = 12 and x = 5
4. Hence, combined yearly return on investment of $100 each at x% and y% can be calculated as

Answer : C

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