Question

five years ago a womans age was the square of his sons age ten years hence her age will be twice that of her sons age find the age of the son five years ago and the present age of the woman

Answer 1

i hope this will usful to u

Answer 2

Answer:

• 5 years.
• 30 years.

Step-by-step explanation:

Given

• Five years ago a woman's age was the square of his son's age.
• Ten years hence her age will be twice that of her son's age.

To find

• Age of son five years ago.
• Present age of the woman.

Solution

Let the son's age 5 years ago be x years.

Then, woman's age 5 years ago will be x² years.

Son's present age = x + 5 years.

Woman's present age = x² + 5 years.

Son's age 10 years hence = x + 5 + 10 = x + 15 years.

Woman's age 10 years hence = x² + 5 + 10 = x² + 15 years.

According to the question, ten years hence (women) age will be twice son's age.

• x² + 15 = 2(x + 15)
• x² - 2x - 15 = 0
• x² - 5x + 3x - 15 = 0
• x(x - 5) + 3(x - 5) = 0
• x - 5 = 0 or x + 3 = 0
• x = 5 or x = -3

Since, age cannot be negative, x = 5

∴

• Son's age 5 years ago = (x) 5 years.
• Present age of woman = (x² + 5) 30 years.