Question

If the sum of ages of a man and his son is 45 years and product of their ages is 350, then their ages are


30,15

33,12

35,10

40,5

​

Answer 1

$\large\bf\underline{Given:-}$

• Sum of ages of man and his son = 45
• product of Thier ages = 350

$\large\bf\underline {To \: find:-}$

• Present age of man and his son.

$\huge\bf\underline{Solution:-}$

Let the present age of man be x year's

Sum of ages of man and his son = 45

So age of his son = 45 - x

✦ According to Question :-

product of ages of man and his son = 350

↣ x( 45 - x ) = 350

↣ 45x - x² = 350

↣ x² - 45x + 350 = 0

↣x² - 35x - 10x + 350

↣ x( x - 35) - 10(x - 35)

↣ (x - 10)(x - 35)

↣x = 10 or x = 35

Age of man x = 35 years

Age of his son 45- x = 45 - 35 = 10 years

So option 3) is correct

$\rule{200}3$

Answer 2

$\sf{\underline{\large{\underline{\orange{Question:-}}}}}$

If the sum of ages of a man and his son is 45 years and product of their ages is 350, then their ages are.

• 30,15
• 33,12
• 35,10
• 40,5

$\sf{\underline{\large{\underline{\orange{Given:-}}}}}$

• Sum of ages of man & son is 45
• product of their ages= 350

$\sf{\underline{\large{\underline{\orange{To\:Find:-}}}}}$

• Their present age=?

$\sf{\underline{\large{\underline{\orange{Solution:-}}}}}$

• Let the age of Man be = X years.
• Age of son = 45-x

Now,

$\sf→ x(45-x)=350\\\sf→ 45x-x^2=350\\\sf→ x^2-45x+350=0( by\: splitting\:method)\\\sf→ x^2-35x-10x+350=0\\\sf→ x(x-35)-10(x-35)=0\\\sf→ (x-35)(x-10)=0\\\sf→ x-35=0, x-10=0\\\sf→ x_{(Man's\:age)}=35, x_{(son's\:age)}=10$

$\rule{220}2$

Hence,

• The age of Man is 35 years
• Age of son is = 10 years