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# At a certain rate of simple interest, a principal becomes three times

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Math Expert
Joined: 02 Sep 2009
Posts: 61243
At a certain rate of simple interest, a principal becomes three times  [#permalink]

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31 Dec 2019, 01:52
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Difficulty:

75% (hard)

Question Stats:

39% (02:00) correct 61% (01:23) wrong based on 33 sessions

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At a certain rate of simple interest, a principal becomes three times in 15 years. In how many years will the principal amount become nine times?

A. 45 years
B. 30 years
C. 60 years
D. 75 years
E. None of these

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Joined: 10 Dec 2017
Posts: 178
Location: India
At a certain rate of simple interest, a principal becomes three times  [#permalink]

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06 Jan 2020, 06:27
1
Bunuel wrote:
At a certain rate of simple interest, a principal becomes three times in 15 years. In how many years will the principal amount become nine times?

A. 45 years
B. 30 years
C. 60 years
D. 75 years
E. None of these

$$3=(1+X/100)^(15)$$
3=1+15X/100
X=200/15
and
$$9=(1+X/100)^q$$
$$9=1+qX/100$$
$$8=qX/100$$
$$q=800/X$$
$$q=800/(200/15)$$
q=60 years
C:)
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At a certain rate of simple interest, a principal becomes three times  [#permalink]

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06 Jan 2020, 06:35
1
Bunuel wrote:
At a certain rate of simple interest, a principal becomes three times in 15 years. In how many years will the principal amount become nine times?

A. 45 years
B. 30 years
C. 60 years
D. 75 years
E. None of these

Given

$$P = 1, t = 15 , r = ? , A = 3 , i = 2$$

Find i -

$$\frac{ptr}{100} = i$$

Or, 1*15*r = 200

Or, r = 13.33 %

We need to find t now

Given $$i = 8 , p = 1 , t =? r = 13$$ (say)

So, $$8 = \frac{1*t*13}{100}$$

Or, $$t$$ ~ $$60$$ , Answer must be (C)
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Re: At a certain rate of simple interest, a principal becomes three times  [#permalink]

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06 Jan 2020, 10:45
2
The SI is always same each year for a principal and same rate of interest.

Using this principle we can infer, if Principal becomes three times in 15 years, then Amount = 3P
However P was already invested , so Cumulative Interest in 15 years is actually I= 2P

now its a simple relation calculation

For Amount to become 9P , I = 8P

I becomes 2P in 15 years
then I becomes 8P in 15*4 = 60 Years

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Re: At a certain rate of simple interest, a principal becomes three times   [#permalink] 06 Jan 2020, 10:45
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