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22 Jan 2017, 01:42
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
55% (02:59) correct
45%
(03:04)
wrong
based on 302
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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%
A. 5%
B. 7.5%
C. 8.5%
D. 10%
E. 17%
Thanks,
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
22 Jan 2017, 11:54
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EgmatQuantExpert
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
29 Jan 2017, 11:14
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Hey,
PFB the official solution.
Given
To Find:
Combined yearly return if $\(100\) each is invested at \(x\)% p.a. and \(y\)% p.a.?
Approach:
Working Out
Answer: C
Thanks,
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
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
Thanks,
Saquib
Quant Expert
e-GMAT
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
