Question

A girl is twice as her sister. Five years hence the product of their ages is 375. Find the present ages. ​

Answer 1

A girl is twice as old as her sister

let sister age be x

girl age = 2x

After five years,

product of ages = 375

(x+5)( 2x+5) = 375

( x+5)( 2x+5) = 5× 5× 5× 3

( x+5) ( 2x +5) = ( 5×3)( 5×5)

compare

x+5 =5×3 = 15

x=10

So, Present age of sister and girl is 10 and 20 years respectively

Answer 2

Given :-

• Girl is Twice as old as her sister.
• Five years hence the product of their ages is 375.

Solution :-

Lets Assume That, Her Sister Present age is = x years.

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

A/q,

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

→ Her Sister 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,

→ Her sister Present Age = x years = 10 years.

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

So, Girl is 20 years old now, and her sister is 10 years old now.