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# A man took a loan under simple interest. What was the rate of interest

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A man took a loan under simple interest. What was the rate of interest  [#permalink]

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10 Jul 2017, 02:38
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A man took a loan under simple interest. What was the rate of interest?

(1) The number of years for which the loan was taken was the same as the rate of interest.
(2) The final value of the loan after the duration of loan was 9 percent higher than the amount taken as loan.

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A man took a loan under simple interest. What was the rate of interest  [#permalink]

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Updated on: 11 Jul 2017, 06:53
Bunuel wrote:
A man took a loan under simple interest. What was the rate of interest?

(1) The number of years for which the loan was taken was the same as the rate of interest.
(2) The final value of the loan after the duration of loan was 9 percent higher than the amount taken as loan.

stat 1: clearly not suff

stat 2 : the 9 % account for the total interest..but we dont know the number of years,,hence not suff

combined.... given that the amount becomes 9 percent higher and the rate of interest is same as number of years...
the final equation will consist of 1 variable and can be solved,,
ans C

Originally posted by mohshu on 10 Jul 2017, 09:20.
Last edited by mohshu on 11 Jul 2017, 06:53, edited 1 time in total.
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Re: A man took a loan under simple interest. What was the rate of interest  [#permalink]

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10 Jul 2017, 10:23
1 is clearly not sufficient

2 leads to the equation: (1+X%/100)^N = 1.09 -> 2 variables, 1 equation -> infinite answers

1+2: Combining both, we guarantee that X=N, therefore 1 variable + 1 equation -> 1 answer

C
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Re: A man took a loan under simple interest. What was the rate of interest  [#permalink]

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10 Jul 2017, 11:38
Given info : Loan taken under SI.
Find R?

Statement 1 :
Rate = Time
i.e. R=T=r
SI = (P*r*r)/100 --> (100*SI)/P = r^2
Because we have no information about the value of SI and P statement 1 is Not sufficient.

Statement 2:
Final Amount after the given duration is 9% higher then the principal
Final Amount = Principal + SI
Putting the values in statement and forming the equation gives:
(P + (P*R*T)/100) = (P + (9P/100)) --> Taking P common and canceling it gives us --> (1+RT/100) = (1+9/100) --> RT = 9
Here R and T can have multiple values therefore the statement 2 is Not sufficient.

Combine 1 & 2
R=T=r and RT = 9
we have r^2 = 9
r = +3 and -3

As rate and time cannot be negative we will consider only the positive root i.e. R=T=r=3
Therefore sufficient

Hence answer = C
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Re: A man took a loan under simple interest. What was the rate of interest  [#permalink]

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10 Jul 2017, 11:45
vituutiv wrote:
1 is clearly not sufficient

2 leads to the equation: (1+X%/100)^N = 1.09 -> 2 variables, 1 equation -> infinite answers

1+2: Combining both, we guarantee that X=N, therefore 1 variable + 1 equation -> 1 answer

C

I am a bit confused with the explanation of statement 2.
Even-though the final answer should be C the explanation seems not right.
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A man took a loan under simple interest. What was the rate of interest  [#permalink]

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10 Jul 2017, 14:38
tusharkhale wrote:
vituutiv wrote:
1 is clearly not sufficient

2 leads to the equation: (1+X%/100)^N = 1.09 -> 2 variables, 1 equation -> infinite answers

1+2: Combining both, we guarantee that X=N, therefore 1 variable + 1 equation -> 1 answer

C

I am a bit confused with the explanation of statement 2.
Even-though the final answer should be C the explanation seems not right.

I just realized it's simple interest, not compound. That's probably why you were confused.
The equation changes, but the reasoning is the same.
The equation derived from (1) is, in fact:

P*(1+X*N) = P*1.09 -> (1+X*N) = 1.09 -> 2 variables, 1 equation
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Re: A man took a loan under simple interest. What was the rate of interest  [#permalink]

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10 Jul 2017, 18:32
From 1, prt = P*r*r no other info, so inufficient

From 2, prt = 1.9p

Insufficient

1+2
P*r*r = 1.9P
R= sq.root 1.9

Hence, C.

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Re: A man took a loan under simple interest. What was the rate of interest  [#permalink]

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11 Jul 2017, 00:01
Simple interest formula: I=Prt (P=principal, r=rate, t=time)
Question asks what is r?

1) Given that t=r, e.g. if t=10 years, then r=10%. The formula then becomes I=P*(r/100)*r or I=Pr^2/100. Not sufficient to find r.

2) Given that final value of the loan is 9% higher than initial value. Thus final value of loan = (P+I)/P = 1.09. The formula can be rewritten as:
(P+Prt)/P=1.09. Not sufficient as we don't know P or t in order to get r.

Combining 1 and 2, we get P+(Pr^2/100)/P=1.09 or P(100+r^2)/P=1.09. P cancels out so we have 100+r^2=1.09. Now we can find r hence C.
Re: A man took a loan under simple interest. What was the rate of interest   [#permalink] 11 Jul 2017, 00:01
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# A man took a loan under simple interest. What was the rate of interest

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