Question

The simple interest on Rs. 18200 from March 9, 2001 to May 21, 2001 at \[7\dfrac{1}{2}\% \] rate will be
A. Rs. 290
B. Rs. 273
C. Rs. 288
D. Rs. 225

Answer 1

Hint: First, we will calculate the actual time in years and then use the formula of simple interest, \[{\text{S.I.}} = \dfrac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}\], where \[{\text{P}}\] is principal starting amount of money, \[{\text{T}}\] is the interest rate per year and \[{\text{R}}\] is the time the money is invested in years. Then we will substitute the value to find the required value.

Complete step-by-step answer:
First, we will calculate the time from March 9, 2001, to May 21, 2001.

\[
  {\text{Time from March 9,2001 to May 21, 2001}} = 22{\text{ days of March + 30 days of April + 21 days of May}} \\
   = 73{\text{ days}} \\
\]
Since the simple interest is calculated with years, we will find the above 73 days in years.

\[\dfrac{{73}}{{365}}{\text{ years}} = \dfrac{1}{5}{\text{ years}}\]

Simplifying the rate \[7\dfrac{1}{2}\% \], we get
\[7\dfrac{1}{2} = \dfrac{{15}}{2}\% \]

Now, we will find the simple interest, \[{\text{S.I.}} = \dfrac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}\] on Rs 18200 at rate \[\dfrac{{15}}{2}\% \] in \[\dfrac{1}{5}\] years.

\[
  {\text{S.I.}} = \dfrac{{18200 \times \dfrac{{15}}{2} \times \dfrac{1}{5}}}{{100}} \\
   = \dfrac{{18200 \times \dfrac{3}{5}}}{{100}} \\
   = \dfrac{{27300}}{{100}} \\
   = 273 \\
\]

Therefore, the simple interest on Rs. 18200 from March 9, 2001 to May 21, 2001 is Rs. 273.

Hence, option B is correct.

Note: In this question, we will calculate the time and then substitute the values in the formula for simple interest carefully. Also, the values should be in terms of years to find the simple interest. Then use the given conditions and values given in the question, and substitute in the given equation, to find the required value. Also, we are supposed to write the values properly to avoid any miscalculation.