Question

The age of Divyesh's mother is 3 years less than the square of Divyesh's age. The sum of their ages is 53 years. How old is Divyesh's mother

Answer 1

Given :

• The age of Divyesh's mother is 3 years less than the square of Divyesh's age.
• The sum of their ages is 53 years.

To find :

• Age of Divyesh's mother.

Solution :

Consider,

• Present age of his mother = x years
• Present age of Divyesh = y years

According to the 1st condition :-

• The age of Divyesh's mother is 3 years less than the square of Divyesh's age.

$\to\sf{x=y^2-3................(i)}$

According to the 2nd condition :-

• The sum of their ages is 53 years.

$\to\sf{x+y=53..................(ii)}$

$\to\sf{y^2-3+y=53\:[put\:x=y^2-3\: from\:eq(1)]}$

$\to\sf{y^2+y=53+3}$

$\to\sf{y^2+y=56}$

$\to\sf{y^2+y-56=0}$

$\to\sf{y^2+(8-7)y-56=0}$

$\to\sf{y^2+8y-7y-56=0}$

$\to\sf{y(y+8)-7(y+8)=0}$

$\to\sf{(y+8)(y-7)=0}$

Either,

y+8=0

→ y = -8

Or,

y-7=0

→ y = 7

• Present age of Divyesh = 7 years

Now , put y = 7 in eq (ii).

$\to\sf{x+y=53}$

$\to\sf{x+7=53}$

$\to\sf{x=53-7}$

$\to\sf{x=46}$

Therefore, the age of Divyesh's mother is 46 years.