Question

Nishtha borrowed Rs.1000 at 10 percent per annum simple interest from a co operative society on January 1 , 1997. She cleared the loan by paying Rs.1020. The amount was paid on
a.March 15,1997
b.March 13.1997
c.March 16,1997
d.March 14,1997

Answer 1

Hint: Given that she borrowed the money on January 1 ,1997 . so the principal amount is Rs.1000 and the final amount paid is 1020 and the rate of interest is 10% so we can find the number of years using the simple interest formula $A = P\left( {1 + \dfrac{{nr}}{{100}}} \right)$ and after obtaining n we need to convert it into months by multiplying by 12 and further multiply by 30 to get the number days and adding it to the day the money was borrowed we get the day the loan was paid.

Complete step-by-step answer:
We are given that the money was borrowed on a simple interest of 10 percent
And the principal amount is Rs.1000
The formula of simple interest is $A = P\left( {1 + \dfrac{{nr}}{{100}}} \right)$
And the principle amount, P is Rs.1000
Here the total amount , A is Rs.1020
Here the rate of interest is 10%
The number of years , n is unknown .
So lets substitute the values in the formula
$
   \Rightarrow 1020 = 1000\left( {1 + \dfrac{{10r}}{{100}}} \right) \\
   \Rightarrow 1020 = 1000\left( {\dfrac{{100 + 10n}}{{100}}} \right) \\
   \Rightarrow 1020 = 10\left( {100 + 10n} \right) \\
   \Rightarrow \dfrac{{1020}}{{10}} = \left( {100 + 10n} \right) \\
   \Rightarrow 102 = 100 + 10n \\
   \Rightarrow 102 - 100 = 10n \\
   \Rightarrow 2 = 10n \\
   \Rightarrow \dfrac{2}{{10}} = n \\
   \Rightarrow n = \dfrac{1}{5} \\
$
Therefore we get the number of years to be $\dfrac{1}{5}$
So to convert it into months we need to multiply by 12 as 12 months make one year
$\begin{gathered}
   \Rightarrow \dfrac{1}{5}*12 \\
   \Rightarrow 2.4 \\
\end{gathered} $
Here we get 2.4 months and once again we need to convert the 0.4 months into days
To convert month into days we need to multiply by 30 as 30 days make a month
$ \Rightarrow 0.4*30 = 12days$
Therefore the number of days she took to pay the amount is 2 months and 12 days
She borrowed the money on January 1,1997
So now after two months and 12 days the day she paid the loan is march 13,1997
The correct option is b.

Additional information :
Simple interest is calculated by multiplying the daily interest rate by the principal, by the number of days that elapse between payments.
Simple interest benefits consumers who pay their loans on time or early each month.
Auto loans and short-term personal loans are usually simple interest loans.

Note: We convert the years to months and days just because we are asked for the date when the amount was returned . If not its correct to leave the number of years to be $\dfrac{1}{5}$
Same way to convert days into months we need to divide it by 30 and to convert months into years we need to divide it by 12.