Question

The sum of the ages in years of a son and his father is 35 and the product of their ages in years is 150. Find their present ages

Answer 1

LET THEIR AGES BE X AND Y.
THEN , X+Y = 35 and xy= 150
 
(X-Y)^2 = (X+Y)^2 - 4XY
(X-Y)^2= (35)^2 - 600
(X-Y)^2 =  1225 - 600
(X-Y)^2 = 625
x-y = 25

AGAIN X+Y = 35 AND X-Y = 25
NOW;
(X+Y)+(X-Y)= 60
2X=60
 X=30
NOW ,
Y= 5
SO THEIR PRESENT AGES ARE 30 AND 5.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the age of father be x years.

And the age of son be y years.

According to the Question,

⇒ x + y = 35 and xy = 150

⇒ y = 35 - x

Putting y's value in xy = 150

⇒ x(35 - x) = 150

⇒ x² - 35x + 150 = 0

⇒ (x - 30) (x - 5) = 0

⇒ x = 30, 5 (Rejected)

⇒ y = 5

Hence, the age of father is 30 years and the age of son is 5 years.