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 :-

• Age of man is 3 times as his sister's age.
• Product of their ages before eight years = 112 years

To find :-

• Present age of man?

Solution :-

⌬ Let age of his sister be x years.

⌬ Then, age of man is 3x years.

Eight years ago,

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

★ Now, According to the Question:

➻ (x - 8)(3x - 8) = 112

➻ (-8)² + (x + 3x)(-8) + (x)(3x) = 112

➻ 64 - 32x + 3x² = 112

➻ 3x² - 32x = 112 - 64

➻ 3x² - 32x = 48

➻ 3x² - 32x - 48 = 0

➻ 3x² - 36x + 4x - 48 = 0

➻ 3x(x - 12) + 4(x - 12) = 0

➻ (x - 12)(3x + 4) = 0

➻ x = 12 , -4/3

Since, age of his sister can't be negative.

So, x = 12

Therefore,

• Present age of his sister, x = 12 years
• Present age of man, 3x = 3 × 12 = 36 years

Answer 2

✯ Given :-

A man's age is 3 times as his sister's age.

• Eight years ago the product of their age was 112 years.

✯ To Find :-

• What is the age of the man presently.

✯ Solution :-

❒ Let the age of his sister be x

❒ And the age of man is 3x

⋆ Before eight years ago their age will be,

◪ Age of his sister = (x - 8) years

◪ Age of the man = (3x - 8)

➣ According to the question,

⇒ (x - 8)(3x - 8) = 112

⇒ 3x² - 8x - 24x + 64 = 112

⇒ 3x² - 32x + 64 - 112 = 0

⇒ 3x² - 32x - 48 = 0

⇒ 3x² - (36 - 4)x - 48 = 0

⇒ 3x² - 36x + 4x - 48 = 0

⇒ 3x(x - 12) + 4(x - 12) = 0

⇒ (x - 12) = 0 ; (3x + 4) = 0

⇒ x - 12 = 0 ; 3x + 4 = 0

⇒ x = 12 ; x = - $\dfrac{4}{3}$

➥ x = 12 ; - $\dfrac{4}{3}$

➛ Since, the age can't be negetive.

Hence,

◈ The present age of sister's = x = 12 years

◈ And, the present age of man = 3x = 3(12) = 36 years.

$\therefore$ The present age of sister's be 12 years and the present age of man will be 36 years .

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