Question

a man's age is 3 times as his sister's age.Eight years ago,the product of their age was 112years. what is the age of the man presently​

Answer 1

Given Parameters :-

A man's age is 3 times as his sister's age.Eight years ago,the product of their age was 112 years.

Unknown :-

• Present Age of man = ?

Solution :-

Let the age of man's sister be x years

Therefore, the age of man will be 3x years

☆ Eight years ago,

• Age of his sister = (x - 8) years
• Age of man = (3x - 8) years

☆ Product of their ages = 112

★ According to Question now,

➝ (x - 8)(3x - 8) = 112

➝ 3x² - 8x - 24x + 64 = 112

➝ 3x² - 32x + 64 = 112

➝ 3x² - 32x + 64 - 112 = 0

➝ 3x² - 32x - 48 = 0

By using splitting middle term we get :

➝ 3x² - 36 + 4x - 48 = 0

➝ 3x(x - 12) + 4(x - 12) = 0

➝ (3x + 4) (x - 12)

➝ x = - ⁴/₃ or x = 12

Therefore, Ignoring negative value x = 12.

Hence,

• Present Age of man = 3x = 3(12) = 36 years