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# A certain amount becomes 31/30 th of itself in 1/9 years

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Director
Joined: 18 Dec 2017
Posts: 853
Location: United States (KS)
A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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27 Nov 2019, 09:45
1
00:00

Difficulty:

65% (hard)

Question Stats:

52% (01:46) correct 48% (01:51) wrong based on 23 sessions

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Question: A certain amount becomes 31/30 th of itself in 1/9 years. Find the rate of simple interest?

Options:
(a)30%
(b)20%
(c)25%
(d)32%
(e)19%

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Intern
Joined: 25 Nov 2019
Posts: 18
Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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27 Nov 2019, 11:38
So here is how I solved
A=P(1+rt) A=(31/30)x P=x t=1/9
(31/30)x=x(1+r(1/9)) = 31/30 - 1 = (1/9)r = 1/30*9=r or 3/10 30%
Intern
Joined: 16 Jan 2018
Posts: 1
Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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01 Dec 2019, 19:31
Amount(A)/Principle(P) = 31/30
∴ SI/P (for 1/9 yr) = 1/30
∴ SI/P (for 1 yr)= 9 × 1/30=3/10
So Rate% = 3/10 ×100% = 30%

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Math Expert
Joined: 02 Aug 2009
Posts: 8305
Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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01 Dec 2019, 20:48
TheNightKing wrote:
Question: A certain amount becomes 31/30 th of itself in 1/9 years. Find the rate of simple interest?

Options:
(a)30%
(b)20%
(c)25%
(d)32%
(e)19%

Let the principal be 30, so amount after 1/9 year is 30*31/30=31, so interest =31-30=1.
I=PRT/100.....1=30*R/100*1/9....R=900*1/30=30%
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GMAT 1: 580 Q43 V27
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Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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01 Dec 2019, 23:16
Stonely wrote:
So here is how I solved
A=P(1+rt) A=(31/30)x P=x t=1/9
(31/30)x=x(1+r(1/9)) = 31/30 - 1 = (1/9)r = 1/30*9=r or 3/10 30%

Had you raised the red entity to power > 1, you would have stuck. Its a SI question.
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Senior Manager
Joined: 25 Jul 2018
Posts: 399
Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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01 Dec 2019, 23:37
31/30 —1 = 1/30
—> increasing by 1/30 in 1/9 years
Let's find how much certain amount will increase in one year:

1/30 — 1/9 years
x — 1 year

—> x = (1/30) / (1/9) = 3/10 = 0.3 (Increasing by 0.3 in one year)

—> that means it is 30 %

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Manager
Joined: 16 Feb 2015
Posts: 160
Location: United States
Concentration: Finance, Operations
Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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01 Dec 2019, 23:48
1
TheNightKing wrote:
Question: A certain amount becomes 31/30 th of itself in 1/9 years. Find the rate of simple interest?

Options:
(a)30%
(b)20%
(c)25%
(d)32%
(e)19%

Explanation:
Formula Used: A=P(1+rt)
We have A/P= 31/30
t=1/9, r = ?

Rewriting above formula as: A/P=(1+rt)
Putting values: 31/30=(1 + r*(1/9))
31/30-1 = r * 1/9
1/30 * 9 = r
3/10 = r
r= 0.3 = 30% IMO-A

Please give kudos, if you find my explanation good enough
Manager
Joined: 29 Nov 2018
Posts: 85
Location: India
GPA: 4
WE: Information Technology (Consulting)
Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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01 Dec 2019, 23:52
(P * R * T)/100 = I ------- (1)
P + I = A ------- (2)
Equating value of I in equation (2)
P + PRT/100 = A
P(1 + R/900) = 31/30P
1 + R/900 = 31/30
R/900 = 1/30
R = 30 %
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Hope it helps,

Thanks,
Mofe Bhatia
Re: A certain amount becomes 31/30 th of itself in 1/9 years   [#permalink] 01 Dec 2019, 23:52
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