Question

Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
A) 3.6
B) 6
C) 18
D) Can’t be determined

Answer 1

Hint: We will first write the formula for the simple interest. Now, assume the rate and time period both to be $x$ and put in the formula, we will thus get the required answer.

Complete step by step answer:
We know that Simple interest on some principal amount is given by the following formula
$S.I. = \dfrac{{P \times R \times T}}{{100}}$, where S.I. stands for the simple interest, $P$ stands for the principal amount on which the interest is charged, R is the rate of interest and $T$ is the time period in years.
Now, let us assume that rate of interest ($R$) = Time period ($T$) = $x$. (Because they are given to be equal)
Now, putting in these values in the formula mentioned above, we will thus get the following expression
$ \Rightarrow S.I. = \dfrac{{P \times x \times x}}{{100}}$
Simplifying the RHS a bit, to get the following expression
$ \Rightarrow S.I. = \dfrac{{P \times {x^2}}}{{100}}$
Now, since Reena took the principal amount of Rs. 1200. So, putting this in the above expression to get the following expression
$ \Rightarrow S.I. = \dfrac{{1200{x^2}}}{{100}}$
Simplifying the RHS a bit, to get the following expression
$ \Rightarrow S.I. = 12{x^2}$
Since it is provided to us that she paid $Rs. 432$ at the end of the time period. So, we have
$ \Rightarrow 432 = 12{x^2}$
Rearranging the terms to get
$ \Rightarrow {x^2} = \dfrac{{432}}{{12}}$
Simplifying the RHS to get:
$ \Rightarrow {x^2} = 36$
Hence, we have:
$ \Rightarrow x = \pm 6$.
Since the time period and the rate of interest cannot be negative.
$\Rightarrow x = 6$.

$\therefore$ The rate of interest is 6. Hence, the correct option is (B).

Note:
The students must remember to reject one of the values they obtained at the end because if no value can be rejected due to any reason, there would be two possible answers, and thus, we would not be able to mark any option.
The students must also note that they need as many equations as many unknown variables they have. Like, here we had the only $x$ and thus, one equation was sufficient to solve it.