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# Edward invested five-ninths of his money at an annual rate of 2r% comp

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Director
Joined: 18 Feb 2019
Posts: 591
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

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31 May 2019, 09:13
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Difficulty:

85% (hard)

Question Stats:

52% (03:10) correct 48% (02:59) wrong based on 63 sessions

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Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?

A. 10%
B. 15%
C. 20%
D. 25%
E. 33%
VP
Joined: 19 Oct 2018
Posts: 1080
Location: India
Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

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31 May 2019, 15:01
2
There are 2 approaches to solve this question

1. Alligation Method
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, his total interest would be slightly above 2r%.
We can use allegation method which would give us approximate answer.

2r...................r
.....100/3.........
5....................4

$$\frac{6r-100}{100-3r}$$=4/5
42r=900
r=21 which is closest to 20

2. General Approach
Let principal amount = P

a. 5P/9 is invested at annual 2r% compounded semi-annually
Interest= [5P/9{1+(r/100)}^2] -5P/9
b. 4P/9 is invested at an annual rate of r% compounded annually
Interest= [4P/9{1+(r/100)}]- 4P/9

Total interest=[5P/9{1+(r/100)}^2]-5P/9 + [4P/9{1+(r/100)}]- 4P/9= P/3

Solving above equation, we will get r=20

This approach is a bit lengthy though.

kiran120680 wrote:
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?

A. 10%
B. 15%
C. 20%
D. 25%
E. 33%
Director
Joined: 24 Nov 2016
Posts: 809
Location: United States
Re: Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

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30 Sep 2019, 08:31
kiran120680 wrote:
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?

A. 10%
B. 15%
C. 20%
D. 25%
E. 33%

$$(5x/9)(1+2r/2)^2+(4x/9)(1+r)=(1+1/3)x$$
$$(5x/9)(1+r)^2+(4x/9)(1+r)=(1+1/3)x$$
$$(1+r)[(5x/9)(1+r)+(4x/9)]=(1+1/3)x$$
$$(1+r)[(5x+5xr+4x)/9]=(1+1/3)x$$
$$(1+r)(9x+5xr)=(1+1/3)x(9)$$
$$9x+5xr+9xr+5xr^2=(1+1/3)(9)(x)$$
$$9+14r+5r^2=1.333(9)$$
$$5r^2+14r+9(1-1.333)=0$$
$$5r^2+14r+9(-0.333)=0$$
$$5r^2+14r-3=0$$
$$(5r-1)(r+3)=0$$
$$r=(1/5,-3)>0=1/5=0.20$$

Intern
Joined: 12 Aug 2019
Posts: 14
Re: Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

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30 Sep 2019, 19:36
nick1816 wrote:
There are 2 approaches to solve this question

1. Alligation Method
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, his total interest would be slightly above 2r%.
We can use allegation method which would give us approximate answer.

2r...................r
.....100/3.........
5....................4

$$\frac{6r-100}{100-3r}$$=4/5
42r=900
r=21 which is closest to 20

2. General Approach
Let principal amount = P

a. 5P/9 is invested at annual 2r% compounded semi-annually
Interest= [5P/9{1+(r/100)}^2] -5P/9
b. 4P/9 is invested at an annual rate of r% compounded annually
Interest= [4P/9{1+(r/100)}]- 4P/9

Total interest=[5P/9{1+(r/100)}^2]-5P/9 + [4P/9{1+(r/100)}]- 4P/9= P/3

Solving above equation, we will get r=20

This approach is a bit lengthy though.

kiran120680 wrote:
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?

A. 10%
B. 15%
C. 20%
D. 25%
E. 33%

Intern
Joined: 01 Jun 2019
Posts: 9
Re: Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

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03 Oct 2019, 13:18
1
1
Took me about 4 minutes to solve it, but this is how I did it. (Pardon the poor quality of the scan).
Attachments

699E843E-9331-4EFD-A9EF-846A8F23D6D1.JPG [ 1009.8 KiB | Viewed 280 times ]

Re: Edward invested five-ninths of his money at an annual rate of 2r% comp   [#permalink] 03 Oct 2019, 13:18
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