Question

Manju takes a loan of Rs. 500, from the village moneylender at the rate of 36% per annum and pays back Rs. 680 after some time. How long did Manju take the loan?

Answer 1

Hint: We have to use the formula of simple interest to find the duration of loan taken by Manju. We know the formula for simple interest is given by I = PRt, where P is the principal amount, R is the annual rate of interest in $\%$ and t is the time period in years. So, we will use the data given in the question, substitute in the formula and get the value of t.

Complete step-by-step answer:
We can solve this problem by using the simple interest formula:
Let us assume that, P is our principal amount.
I = our interest amount.
r = rate of interest per year as a percent.
t = time period involved in months or years. In this case it is in the year. Then the formula is:
I = PRt
Here in this problem, we have I=(680-500)=180 , this is the amount she paid as interest.
$P=500,R=36\%$
‘t’ is unknown to us. We have to find out the value of ‘t’ by using the above formula.
Now put these values in the formula:
$\begin{align}
& \Rightarrow 180=500\times \left( 36\% \right)\times t \\
& \Rightarrow 180=500\times \dfrac{36}{100}t \\
& \Rightarrow 180=(5\times 36)t \\
& \Rightarrow 180t=180 \\
\end{align}$
Now, divide both side of the equation by 180, we get
t = $\dfrac{180}{180}$ = 1
Therefore, Manju took the loan for one year.

Note: There is another approach to solve this question. It is given in the question that a person named Manju takes a loan at the rate of 36% per annum. That means she has to pay back Rs. 36 per Rs. 100 in one year. So for Rs. 500 she has to pay Rs. $(36\times 5)=180$ per annum or per year. That means she has to pay Rs. 180 as interest per year. It is given in the question that she paid Rs. 680 after some time. So she paid Rs.(680-500)=180 extra as interest. This is exactly the same as the amount of one year interest. That means she paid her money back exactly after one year. Therefore Manju took the loan for one year.