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

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Answer 1

Answer:

Option numberC: 35,10

Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Sum of ages of man and his son is = 45 years

• Product of Thier ages is = 350

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What are their present ages?

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Let the present age of man be x years.

As per question :-

Given that,

Sum of ages of man and his son is = 45 years

Therefore, age of his son will be = ( 45 - x) years

Again, it's given that

product of ages of man and his son is = 350

According to the question ;-

⟶ x( 45 - x ) = 350

⟶ 45x - x² = 350

⟶ x² - 45x + 350 = 0

⟶ x² - 35x - 10x + 350 = 0

⟶ x( x - 35) - 10(x - 35) = 0

⟶ (x - 10)(x - 35) = 0

⟶ x = 10 Or, ⟶ x = 35

Hence,

Age of man = 35 years

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

_________________________________________

Verification :-

Given that,

Product of Their ages is = 350

⟶ 35 × 10 = 350

⟶ 350 = 350

L.H.S = R.H.S

Hence, verified