Question

in a family of father ,son and daughter
age of father is twice the average age of the whole family
age of daughter is half the average age of family
if son is ten years old ,what is average age of family​

Answer 1

Answer:

The average age of the family is 20 years.

Step-by-step explanation:

Given:

• Age of son = 10 years

• Age of father is twice the average age of the whole family

• Age of daughter is half the average age of family

Let the age of father be x and the age of the daughter be y

According to the conditions given in the question,

x = 2 * $\frac{x+10+y}{3}$

=> 3x = 2x + 20 + 2y

=> 3x - 2x - 2y = 20

=> x - 2y = 20                           --(i)

and y = ($\frac{1}{2}$) * $\frac{x+10+y}{3}$

=> 6y = x + 10 + y

=> 6y - y - x = 10

=> 5y - x = 10                    --(ii)

Solving equation (i) and equation (ii),

 x - 2y = 20

-x + 5y = 10

On adding,

3y = 30

=> y = 10

Therefore, age of daughter = 10 years

Substituting the value of x in equation (i)

=> x - 2*10 = 20

=> x - 20 = 20

=> x = 20 + 20

=> x = 40

Therefore, age of father = 40 years

Average age of family = $\frac{Sum of ages}{No.of members}$

                                     = $\frac{40+10+10}{3}$

                                     = $\frac{60}{3}$

                                     = 20

Therefore, the average age of the family is 20 years.