Question

The sum of money that will give \[{\rm{Rs}}\;1\] as simple interest per day at the rate of \[5\% \] p.a. is.
A. Rs. 730
B. Rs.3650
C. Rs. 7300
D. Rs. 36500

Answer 1

Hint: Here it is given that \[{\rm{Rs}}\;1\] is the simple interest per day, but the rate is given for annum, so find the simple interest for annum by multiplying the \[{\rm{Rs}}\;1\] with the number of days in a year that means 365 days, then we will get the simple interest as 365 days, now we can substitute the values in the principal formula to find the sum of money.

Complete step-by-step answer:
The simple interest per day is Rs. 1, then the simple interest per year that consists of 365 days is \[\begin{array}{c}
S.I = {\rm{Rs}}\,1 \times 365\\
 = {\rm{Rs}}\,365
\end{array}\]
The rate of sum per annum is \[R = 5\% \]
The time given for the sum to repay is \[t = 1\,{\rm{year}}\].
Assume P is the principal sum that I need to find.
The simple interest is defined as the ratio of the product of principal sum, time taken to repay and rate for which the sum is lent to the 100.
The equation to find the sum of the money is
\[S.I = \dfrac{{PTR}}{{100}}\]
Substituting the values in the given equation, then we will get
\[\begin{array}{c}
S.I = \dfrac{{PTR}}{{100}}\\
365 = \dfrac{{P \times 1 \times 5}}{{100}}\\
P = \dfrac{{365 \times 100}}{5}\\
 = 7300
\end{array}\]
Therefore, the sum of the money that will give Rs. 1 per day is Rs7300, it means the option (C) is correct.
So, the correct answer is “Option C”.

Note: Here, we have to be careful at the simple interest because it is given only for 1 day, but the rate is provided for 1 annum, so we have to convert the simple interest for 1 year to get the sum of money then we will get the correct answer. If we blindly substitute the simple interest of Rs1 in the formula, then we will get the wrong answer.