Question

The difference between the ages of a man and his son is 25 years now. If the product of the numbers denoting their ages, ten years back, be 150, find the present age of the father.

Answer 1

Answer: 40 yrs

Step-by-step explanation:

Let the age of father is x yrs

The age of the son is (x-25)yrs

According to the question,

(x-10)(x-25-10) = 150

⇒(x-10)(x-35) = 150

⇒x^2-45x+350=150

⇒x^2-45x+200=0

⇒x^2-40x-5x+200 = 0

⇒x(x-40) - 5(x-40) = 0

⇒(x-5)(x-40)=0

x= 5 or x =40

But x cannot be 5 because if x = 5 then Son's age becomes -20 which is impossible.

∴ The age of the father is 40yrs.

Answer 2

Let Age of Man =x

Let Age of his Son=y

Given difference=25 years

Means

x-y=25

x=25+y

Ten Years Back

Father age was=(x-10) years

Son age was=(y-10) years

THEIR product=150

(x-10)(y-10)=150

x=25+y

(25+y-10)(y-10)=150

(15+y)(y-10)=150

15y-150+y²-10y=150

y²+5y-150=150

y²+5y-150-150=0

y²+5y-300=0

By Middle Term Splitting

Prime Factors of 300=3×2×5×2×5

5y can written as=20y-15y

So,

y²+5y-300

y²+20y-15y-300=0

y(y+20)-15(y+20)

(y-15)(y+20)=0

Means

y-15=0

y=15

y+20=0

y=-20

As Age can't be in Negative

So Age of Son=y=15 years

Father Age=x=25+y=25+15=40 years

$\boxed{\mathbf{\huge{Father=40\:years}}}$