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

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

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New post 27 Nov 2019, 09:45
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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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Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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New post 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%
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Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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New post 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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Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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New post 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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Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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New post 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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Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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New post 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 %

The answer is A

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Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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New post 01 Dec 2019, 23:48
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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 Please give kudos, if you find my explanation good enough :please
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Re: A certain amount becomes 31/30 th of itself in 1/9 years  [#permalink]

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