Question

4. 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

ATQ, a girl is twice as old as her sister.

let her sister's age be x

therefore her age = 2x

5 years after, the product of their ages will be 375

➡ (5 + x)(5 + 2x) = 375

➡ 5(5 + 2x) + x(5 + 2x) = 375

➡ 25 + 10x + 5x + 2x² = 375

➡ 25 + 15x + 2x² = 375

➡ 2x² + 15x = 375 - 25

➡ 2x² + 15x = 350

➡ 2x² + 15x - 350 = 0

using splitting middle term method,

= 2x² + (35x - 20x) - 350

= 2x² + 35x - 20x - 350

= x(2x + 35) - 10(2x + 35)

= (2x + 35) (x - 10)

equating both factors by 0

• 2x + 35 = 0

➡ x = -35/2

• x - 10 = 0

➡ x = 10

since age can't be negative.

hence, her sister's age is = x =10 years

and her age is = 2x = 2 × 10 = 20 years

Answer 2

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