Question

There is a happy family consisting of 2 parents and kids. The average age of the family is 20. But if we exclude one parent whose age is 40, the average age of the family drops to 15. Find the number of kids in the family.  

Answer 1

Suppose there are n people in this family
one parent is age 40, suppose the rest of the family add up to be y years old
the average is (40+y)/n=20  =>40+y=20n
 exclude the 40-year-old parent, the sum of age is still y, the number of family is (n-1), the average is y/(n-1)=15 =>y=15n-15
substitute y=15n-15 in the first equation: 40+(15n-15)=20n
solve for n: 5n=25, n=5
there are a total of 5 people in this family, there are 3 kids.

Answer 2

Let k be the number of kids. Size of family = 2 + k.
Total of all the ages = 20(2 + k).
Total of all the ages excluding 40 year old parent = 20(2 + k) - 40 = 20k.
15 = 20k/(1 + k)
15 + 15k = 20k.
k = 3