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 ?  Choose the correct choice from the following options
A) 37
B) 29
C) 11
D) 15
E) 12
Explanation:   i) Let the ages of the five members at present be a, b, c, d &amp; 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) &amp; (e-3) years   So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)   ==&gt; a + b + c + d + e = 5x + 15   ==&gt; 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   ==&gt; (5x + 15 - e + f) = 5x   Solving e - f = 15 years.   Thus the difference of ages between replaced and new member = 15 years.   Answer: 15
<result>D</result>
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 ?