The average age of six members of a family is 40 years. If the age of a guest is included, then the average age increases by 12.5%. What is the age (in years) of the guest?

75

New avg. age after including guest = 40 x 1.125

Sum of ages of all members including guest = 7 x 40 x 1.125

Sum of ages of all member excluding guest = 6 x 40

Age of guest = 7 x 40 x 1.125 - 6 x 40

Age of guest = 40 x ( 7.875 -6 ) = 75 Years