The average age of six brothers is 15 years. If their father is also included, the average is increased by 7 years. Find the age of the father(in years).

64

Average age of the family = $\frac{sum\;of \;ages\;of\;all\;members}{6}$

⇒    15  = $\frac{sum\;of \;ages\;of\;all\;members}{6}$

⇒  Sum of ages of all members = 15 x 6 = 90

Now, if the father's age(say, $x$ years) is added,

Sum of ages of all members = 90 + $x$ 

Then, average becomes (15 + 7) 22

⇒ $\frac{90+x}{7}$ = 22

⇒ 90 + $x$ = 154

⇒      $x$    = 64