Question

The number of members of a club increases by $ 10\% $ every year. If the initial number of members is $ 500 $ , then what will be the number at the beginning of the third year?
 $
  A.\,\,610 \\
  B.\,\,615 \\
  C.\,\,620 \\
  D.\,\,605 \\
  $

Answer 1

Hint: In this type of problem as members are increasing at $ 10\% $ of every year. Therefore we calculate $ 10\% $ of given value and add the result to it to get numbers of members at the end of first year and calculating again $ 10\% $ of members obtained in the end of first year and then adding it back to get total number of members at the end of second year and hence required solution of the given problem.

Complete step-by-step answer:
Given, initial number of members = $ 500 $
Since, it is required to find numbers of members at the start of third year or we can say the number of members increased in two years.
It is given that every year $ 10\% $ of members increased by every year.
Therefore, number of members at the end of one year is given as: $ 500 + 10\% \,\,of\,\,500 $
  $
   = 500 + \dfrac{{10}}{{100}} \times 500 \\
   = 500 + \dfrac{1}{{10}} \times 500 \\
   = 500 + 50 \\
   = 550 \;
  $
Hence, we see that numbers of members at the end of first year or beginning of second year are $ 550 $ .
Since, members are increasing by $ 10\% $ every year.
Therefore, number of members at the end of second year given as: $ 550 + 10\% \,\,of\,\,550 $
 $
   = 550 + \dfrac{{10}}{{100}} \times 550 \\
   = 550 + \dfrac{1}{{10}} \times 550 \\
   = 550 + 55 \\
   = 605 \;
  $
Hence, from above we see that number of members at the end of second year or at the beginning of third year are $ 605 $ .
Therefore, the correct option is (D).
So, the correct answer is “Option D”.

Note: We can also find the solution of given problem by using compound formula which is given as: $ A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t} $ . In this we can take P as number of initial members, r as percentage increase and t is given time and substituting values in it to get required solution of problem or we can say number of member at beginning of third year.