Question

A father’s present age is 5 times the sum of ages of his two children. After 7 years his age will be twice the sum of the ages of his two children. Find the age of the father.

Answer 1

Answer:

Let the age of father =x years

The sum of the age of 2 children =y years

According to the first condition

⇒x=3y..eq1

After 5 years

⇒ Father's age =x+5

⇒ The sum of ages of his two children =y+10

According to the second condition

⇒x+5=2(y+10)⇒x+5=2y+20

⇒x−2y=15....eq2

Put the value of x from eq1

⇒3y−2y=15⇒y=15

Put y=15 in eq1

⇒x=3×15⇒x=45

Hence, father age =45 years

Answer 2

Now, it is also given, after 5 years, his age will be twice the sum of the ages of his son. Therfore, after 5 years age of father will be 3(x+y)+5 and age of the sons will be x+5 and y+5. Thus the age of the father is 45.