Thursday, 3 November 2011

Algebra-23 (Ages) (NASSCOM- Sample Problems)

When I was married 10 years ago, my wife was the sixth member in the family. Today my father died, and a baby was born to me. The average age in my family today is what it was when I married. How old my father when he died?
(1) 50 years    (2) 60 years    (3) 70 years    (4) Indeterminate
Solution follows here:
Solution:
Number of family members 10 years ago = 6
Number of family members today is also 6 (one plus for baby and one minus for father)
Let father’s age 10 years ago = F
Let sum of ages of all family members (except Father) 10 years ago = X
Average age of all family members 10 years ago = (F+X)/6                  ---(1)

Today, after 10 years from the earlier point, rest all 5 members’ age is incremented by 10 years each, and new baby with age ‘0’,
Sum of ages of all family members today = (X+50) + (0) = X+50
Average of ages of all family members today = (X+50)/6                       ---(2)

Given that, “average age in my family today is what it was when I married”
=> (1) and (2) are equal
=> F+X = X+50 => F = 50, But this is not the final answer. F is the age of father 10 years ago.
Age of Father when he died = F+10 = 60