Find the simple interest and the amount on ₹. $ 2400 $ for $ 3\,\,years\,\,5\,\,months\,\,and\,\,15\,\,days $ at the rate of 9% per annum.

Hint: For this type of a problem in which rate is given in per annum and time is given is in years, months and in days. So, we can’t apply these values in a formula of simple interest. To get the solution of the problem we first convert given time in years and then using values in a formula of simple interest to get a solution of the required problem.
Formulas for simple interest (S.I.) is given as: $ S.I. = \dfrac{{P \times R \times T}}{{100}} $ , where P is principal , R is rate per annum and T is time in years.

Complete step-by-step answer:
From statement we have,
Amount on which interest is to be calculated is called principal.
Therefore, $ P = $ ₹. $ 2400 $
Rate of interest = 9% per annum.
Time period for which interest is to be calculated = $ 3\,\,years\,\,5\,\,months\,\,and\,\,15\,\,days $
From above we see that rate is in per annum but time is in years, months and in days.
Therefore, we first convert time into years.
We know that there are $ 12\,\,months $ in a year.
Therefore, $ 5\,\,months\,\, = \dfrac{5}{{12}}\,\,years $
Also, there are $ 365\,\,days $ in a year.
Hence, $ 15\,\,days\,\, = \dfrac{{15}}{{365}}\,\,years $
Therefore, from above we see that total time in years becomes: $ 3 + \dfrac{5}{{12}} + \dfrac{{15}}{{365}} $
On simplifying the above term. We have
\[
T = 3 + \dfrac{5}{{12}} + \dfrac{3}{{73}}\,\,\,\,\left( {taking\,\,L.C.M.} \right) \\
\Rightarrow T = \dfrac{{3\left( {12} \right)\left( {73} \right) + 5\left( {73} \right) + 3\left( {12} \right)}}{{\left( {12} \right)\left( {73} \right)}} \\
 \Rightarrow T = \dfrac{{2628 + 365 + 36}}{{876}} \\
 \Rightarrow T = \dfrac{{3029}}{{876}}\left( { \approx 3.46} \right) \\
 \]
Also, we know that simple interest is given as: $ S.I. = \dfrac{{P \times R \times T}}{{100}} $
Substituting values in above formula. We have,
\[
 \text{Simple interest}(S.I.) = \dfrac{{2400 \times 9 \times 3.46}}{{100}} \\
\Rightarrow \text {Simple interest}(S.I.) = \dfrac{{2400 \times 9 \times 3.46}}{{100}} \\
\Rightarrow \text {Simple interest}(S.I.) = 24 \times 31.14 \\
\Rightarrow \text {Simple interest}(S.I.) = 747.36 \;
 \]
Hence, from above we see that a simple interest on a given amount is ₹. $ 747.36\left( { \approx 747} \right) $ .

Note: In simple interest students must see that if rate is in per annum then time will be in years, but if rate is not in per annum then we take time according to that. But for those problems in which the rate is in annum and time is not in years, one must change either rate according to time or time according to rate, whichever seems to be easy to get a solution to the given problem.