The average age of 6 members of a family is 20 years. If the age of the servant is included, then the average age increases by 20%. What is the age of the servant?

48 years 

The average of family's age = $\frac{sum\;of\;ages\;of\;all\;members}{6}$

Sum of ages of all members = 20 x 6 = 120 

Let the age of the servant be $x$ years,

average increases by 20%, new average = 24

Thus, $\frac{120+x}{7}$ = 24

$120 + x = 168$

$x$ = 48 years