Question

a girl is twice as old as her sister .five years hence the product of their ages in yrs will be 375 .find their present ages.​

Answer 1

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Answer 2

Answer:

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