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  • Question
  • After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?


  • Options
  • A. 12
  • B. 13
  • C. 14
  • D. 15

  • Correct Answer
  • 15 

    Explanation

    i) Let the ages of the five members at present be a, b, c, d & e years. 

    And the age of the new member be f years. 

    ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1) 

    iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years 

    So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2) 

    ==> a + b + c + d + e = 5x + 15 

    ==> a + b + c + d = 5x + 15 - e ------ (3) 

    iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above, 

    The new average is: (5x + 15 - e + f)/5 

    Equating this to the average age of x years, 3 yrs, ago as in (2) above, 

    (5x + 15 - e + f)/5 = x 

    ==> (5x + 15 - e + f) = 5x 

    Solving e - f = 15 years. 

    Thus the difference of ages between replaced and new member = 15 years.


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