Question

A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find their present ages.​

Answer 1

Step-by-step explanation:

Given :-

Boy is Twice as old as his Brother.

Five years hence the product of their ages is 375.

Solution :-

Lets Assume That, His brother Present age is = x years.

Than, Boy Present age = 2 * x = 2x years.

A/q,

→ After 5 years His brother will be = (x + 5) years old.

→ Boy will be = (2x + 5) years old.

So,

→ (x + 5) * (2x + 5) = 375

→ 2x² + 5x + 10x + 25 = 375

→ 2x² + 15x + 25 - 375 = 0

→ 2x² + 15x - 350 = 0

Splitting The Middle Term now,

→ 2x² - 20x + 35x - 350 = 0

→ 2x(x - 10) + 35(x - 10) = 0

→ (x - 10)(2x + 35) = 0

Putting both Equal to Zero now,

→ x - 10 = 0

→ x = 10

Or,

→ 2x + 35 = 0

→ 2x = (-35)

→ x = (-35/2) ≠ Negative Value of age Not Possible.

Hence,

→ His Brother Present Age = x years = 10 years.

→ And, Boy Present Age = 2x years = 2*10 = 20 years.

So,

Boy is 20 years old now, and His brother is 10 years old now.

Answer 2

• The age of the girl is = 20 years old
• Her sister = 10 years old

Step-by-step explanation:

Let,

• The present age of the girl be '2x'
• The present age of her sister be 'x'

(as the girl is twice as her sister)

Five years hence,

• Their present will be (2x + 5) and (x + 5)
• The girl will be (2x + 5)
• Her sister will be (x + 5)

Given,

• (2x + 5) (x + 5) = 375

Solving,

⟼ 2x² + 10x + 5x + 25 = 375

⟼ 2x² + 15 + 25 - 375 = 0

⟼ 2x² + 15x - 350 = 0

On factorizing,

⟼ (x - 10) (2x + 35) = 0

⟼ x = 10 , 2x = -35

⟼ x = 10 , x = -35 / 2

Since, age cannot be negative, therefore x = 10.

Hence,

• The age of the girl is = 2x = 2 (10) = 20 years old
• Her sister = 10 years old