Question

One year ago father's age was 8 times of child's age. Now father's age is the square of the child's age. Find the ages of child and father.​

Answer 1

Step-by-step explanation:

Let the present age of the son be x.

Let the father's present age be y.

One year ago, y−1=8(x−1)

⇒y−1=8x−8

⇒y=8x−7

Now applying the condition, we get

(8x−7)=x

2

⇒x

2

−8x+7=0

⇒(x−1)(x−7)=0

⇒x=1 or x=7

Hence, the present age of son is either 1 year or 7 years.

Answer 2

Let the present age of the son be x.

Let the father's present age be y.

One year ago, y−1=8(x−1)

⇒y−1=8x−8

⇒y=8x−7

Now applying the condition, we get

(8x−7)=x^2

 ⇒x^2 −8x+7=0

⇒(x−1)(x−7)=0

⇒x=1 or x=7

Hence, the present age of son is either 1 year or 7 years.