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Word Problem - A $200 investment at x percent per annum and a $500 inv

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Word Problem - A $200 investment at x percent per annum and a $500 inv [#permalink] New post   22 Jan 2017, 01:42
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Q.)
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%


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Word Problem - A $200 investment at x percent per annum and a $500 inv [#permalink] New post   Updated on: 29 Jan 2017, 12:05
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The official solution has been posted. Looking forward to a healthy discussion..:)

Originally posted by EgmatQuantExpert on 22 Jan 2017, 01:43.
Last edited by EgmatQuantExpert on 29 Jan 2017, 12:05, edited 1 time in total.
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Re: Word Problem - A $200 investment at x percent per annum and a $500 inv [#permalink] New post   22 Jan 2017, 11:54
EgmatQuantExpert wrote:
Q.)
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%


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200x+500y= 10%of 700
200x+500y= 70----(A)
Also
400x+600y= 9.20%of 1000
400x+600y= 92----(B)

equating A & B we get x=5% and Y=12%
thus avg. interest on both investments
17/2 =8.5%
Ans C
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Re: Word Problem - A $200 investment at x percent per annum and a $500 inv [#permalink] New post   29 Jan 2017, 11:14
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Hey,

PFB the official solution. :)


Given
    • Case-I
      o Principal ,\(P1 =\) $\(200\)
      o Rate of interest = \(x\)% p.a.
      o Principal, \(P2 =\)$\(500\)
      o Rate of Interest = \(y\)% p.a.
      o Combined yearly return\(= 10\)%

    • Case-II
      o Principal, \(P3 =\) $\(400\)
      o Rate of interest = \(x\)% p.a.
      o Principal, \(P4 =\) $\(600\)
      o Rate of Interest = \(y\)% p.a.
      o Combined yearly return = \(9.2\)%

To Find:

Combined yearly return if $\(100\) each is invested at \(x\)% p.a. and \(y\)% p.a.?

Approach:

    • 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.
    • \(200*\frac{R}{100} = 100 * \frac{x}{100} + 100 * \frac{y}{100}\)

Working Out

    1. Case-I
    a. As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation
      i. \(200 * \frac{x}{100} + 500 *\frac{y}{100} = (200 + 500) * \frac{10}{100}\)
      ii. \(2x +5y = 70\)……………..(1)

    2. Case-II
    a. As the combined yearly return is equal to the sum of the returns of individual investments, we can write the following equation
      i. \(400 * \frac{x}{100} + 600 * \frac{y}{100} = (400 + 600) * \frac{9.2}{100}\)
      ii. \(4x +6y = 92\)…..(2)

    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
      a. \(200 *\frac{R}{100}= 100 * \frac{5}{100} + 100 * \frac{12}{100}\)
      b. Combined return = \(8.5\)%

Answer: C


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Re: Word Problem - A $200 investment at x percent per annum and a $500 inv [#permalink] New post   29 Jan 2017, 23:08
Hi,

Why is it 8.5% and NOT 17%?
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Re: Word Problem - A $200 investment at x percent per annum and a $500 inv [#permalink] New post   29 Jan 2017, 23:55
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shrutikrish136 wrote:
Hi,

Why is it 8.5% and NOT 17%?



Hey,

Did you go through the official solution? :)

In step 4, we got following equation -

    4. Hence, combined yearly return on investment of $\(100\) each at \(x\)% and \(y\)% can be calculated as
      a. \(200 *\frac{R}{100}= 100 * \frac{5}{100} + 100 * \frac{12}{100}\)
      After simplying we get,\(2R = 5 + 12\)
      which is results in \(R = \frac{17}{2}\)
      b. And thus the combined return = \(8.5\)%

In the solution, we have considered R to be the combined return. And thus, we have taken it as \(8.5\)% and not \(17\)%.


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Re: Word Problem - A $200 investment at x percent per annum and a $500 inv [#permalink] New post   30 Jan 2017, 07:48
T700ISB wrote:
Hi,

Why is it 8.5% and NOT 17%?



As we got x & y as 5 & 12 % respectivly
so if $100 is invested with these rates the profit will be $5 + $12 = $17
thus avg. =8.5

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Re: Word Problem - A $200 investment at x percent per annum and a $500 inv [#permalink] New post   05 Mar 2023, 22:42
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