Question

7. One year ago, a man was 8 times as old as his son. Now his age is equal to the square
of his son’s age. Find their present ages.

Answer 1

Let the present age of sun is x yrs
Present age of father is x² yrs.
So, one year ago, sun's age = (x - 1) yrs
one year ago , father's age = (x² - 1) yrs

A/C to question,
One year ago, father's age was 8 times of his son
so, x² - 1 = 8(x - 1)
⇒x² - 1 = 8x - 8
⇒x² - 8x + 7 = 0
⇒x² - 7x - x + 7 = 0
⇒x(x - 7) -1(x - 7) = 0
⇒x = 1 and 7
x ≠ 1 because then father's age = 1² = 1 yr = son's age
Hence, present age of sun = 7 yrs
And father's present age = 7² yrs = 49 yrs

Answer 2

HELLO DEAR,

let the present age of son's = x year.
so, present age of father's = x² year.
one year ago son's = (x - 1)year.
one year ago father's = (x² - 1)year.

now,

given, a man was 8 times as old as his son
so,

(x² - 1) = 8*(x - 1)

x² - 1 = 8x - 8

x² - 8x + 7 = 0

x² - 7x - x + 7 = 0

x(x - 7) - 1(x - 7) = 0

(x - 1)(x - 7) = 0

x = 7 , x = 1$\mathbf{[NEGLECT}}$

hence, the present of of som is 7year.
and present age of father = 7²yeaf = 49year.


I HOPE ITS HELP YOU DEAR,
THANKS