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

Question

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.

mohshu · Answer

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

vituutiv · Answer

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

tusharkhale · Answer

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

tusharkhale · Answer

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

vituutiv · Answer

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

spc11 · Answer

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.

Sent from my A0001 using  GMAT Club Forum mobile app

bianalyst · Answer

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.

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

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