Question 413179
Let no. of people in the club = x and average age = y

sum of age of all people = x*y

when a 34yr old leaves and a 63yr old joins, then total age =  x*y -34 + 64 

= x*y + 30 years

average age = (x*y+30)/x 

according to question, 

(x*y +30)/x = y+2 

=> x*y + 30 = x( y+2) 

=> x*y + 30 = x*y +2x

=> 2x = 30

=>x= 15 
 
total no. of people in the club  =  15