Question

Calculate interest on drawings of Mr. Siddhant $ @\;10\% $ p.a. for the year ended 31st March, 2018 in each of the following alternative cases:
Case 1: If he withdrew Rs. $ 6,000 $ in the beginning of each quarter.
Case 2: If he withdrew Rs. $ 6,000 $ at the end of each quarter.
Case 3: If he withdrew Rs. $ 9,000 $ in the middle of each quarter.

Answer 1

Hint: To calculate the interest on drawings of Mr. Siddhant, firstly find the total drawings of Mr. Siddhant in the given period of time and then find the average period and after finding these both, calculate the interest on drawings with help of the following formula:
 $ I = PRT,\;{\text{where}}\;I,\;P,\;R\;{\text{and}}\;T $ are interest, principle amount, interest rate and average time period respectively.

Complete step-by-step answer:
In order to find the interest in all three cases, let us first consider the total drawings or the principal amounts in three cases as $ {P_1},\;{P_2}\;{\text{and}}\;{P_3} $ respectively, then they will be calculated as
 $
  {P_1} = {\text{Rs}}.6,000 \times 4 = {\text{Rs}}{\text{.24,000}} \\
  {P_2} = {\text{Rs}}.6,000 \times 4 = {\text{Rs}}{\text{.24,000}} \\
  {P_3} = {\text{Rs}}{\text{.9,}}000 \times 4 = {\text{Rs}}{\text{.36,000}} \;
  $
Now, calculating the average time for all three cases, we will get
 $
  {T_1} = \dfrac{{12 + 3}}{2} = 7.5\;{\text{months}} \\
  {T_2} = \dfrac{{9 + 0}}{2} = 4.5\;{\text{months}} \\
  {T_3} = \dfrac{{10.5 + 1.5}}{2} = 6\;{\text{months}} \;
  $
Also we have given in the question the rate of interest $ R = 10\% $ which is same for all cases,
So the interest will in all three cases will be given as
 $
  {I_1} = {P_1}R{T_1} = 24,000 \times \dfrac{{10}}{{100}} \times \dfrac{{7.5}}{{12}} = {\text{Rs}}{\text{.1500}} \\
  {I_2} = {P_2}R{T_2} = 24,000 \times \dfrac{{10}}{{100}} \times \dfrac{{4.5}}{{12}} = {\text{Rs}}.900 \\
  {I_3} = {P_3}R{T_3} = 36,000 \times \dfrac{{10}}{{100}} \times \dfrac{6}{{12}} = {\text{Rs}}.1800 \;
  $
So these are the amount of interest Mr. Siddhant will get if he withdraws according to the three cases respectively.

Note: When calculating the principal amount or the total drawings, take care of the time period that is how many times he has withdrawn the amount. Also when finding the interest then remember that the average time period should be divided with twelve.