Question

the sum of the ages of a father and his son is 50 years. Five years ago the product of their ages was 175. Find their Present age

Answer 1

Let the age of son be y years

So, the age of father be x years

x + y = 50

A.T.Q. [According to Question]

=> (x - 5) (y - 5) = 175

=> xy - 5x - 5y + 25 = 175

=> xy - 5(x + y) = 150

=> xy - 5(50) = 150

=> xy - 250 = 150

=> xy = 400

Now,
x + y = 50

Squaring both the sides

(x + y)² = (50)²
=> x² + y² + 2xy = 2500
=> x² + y² + 800 = 2500
=> x² + y² = 1700

Now,
subtracting both the sides from 2xy

x² + y² - 2xy = 1700 - 2xy
=> (x - y)² = 1700 - 800
=> (x - y)² = 900
=> (x - y)² = (30)²
=> x - y = 30

Now, substitude doing

x + y = 50
x - y = 30

=> x + y + x - y = 50 + 30
=> 2x = 80
=> x = 40

So, y = 10

•°• Present age of son = y years
= 10 years

•°• Present age of father = x years
= 40 years

Hope it helps you ♡♡♡
Have a great day ahead...