Let's analyze each statement:

The number of years for which the loan was taken was the same as the rate of interest.
This statement alone is not sufficient to determine the rate of interest. While it tells us that the number of years is equal to the rate of interest, it doesn't provide us with any numerical value to calculate the rate.

The final value of the loan after the duration of the loan was percent higher than the amount taken as loan.
This statement alone is not sufficient either. While it gives us information about the final value of the loan, it doesn't tell us the duration of the loan or provide us with any numerical value to calculate the rate.

Now, let's consider both statements together:

R=T:

From statement 1, we know that the number of years (T) for which the loan was taken is equal to the rate of interest (R).

From statement 2, we know that the final value of the loan after the duration of the loan was 9 percent higher than the amount taken as a loan. This implies that the interest earned over the duration of the loan is 9 percent of the principal amount.

Using the simple interest formula:

I=P⋅R⋅T

Given that

R=T, we can write:
I = P*\(R^2\)

Given that the interest earned is 9 percent of the principal amount:

9 / 100 P = P*\(R^2\)

Solving for (you don't actually have to solve for R. You can just notice that you can solve for R from the above equation)
R:
\(R^2\) = 9/100
R= 3/10

Therefore, both statements together are sufficient to determine the rate of interest.

The correct answer is (C)

Bernard Baah
MS '05, Stanford
GMAT and GRE Instructor
MapAdvantage Prep