A girl is twice as old as her sister. Four years hence , the product of their ages will be 160 . Find their present ages. this question is of quadratic equation
Answers
Answer:
Step-by-step explanation:
Solution :-
Let the present age of hers sister be x years.
And girl's present age be 2x years.
4 years hence :-
Product of their age = (x + 4) (2x + 4)
According to the Question,
⇒ (x + 4) (2x + 4) = 160
⇒ 2x² + 12x - 144 = 0
⇒ x² + 6x - 72 = 0
⇒ x² + 12x - 6x - 72 = 0
⇒ x(x + 12) - 6(x + 12) = 0
⇒ (x + 12) (x - 6) = 0
⇒ x + 12 = 0 or x - 6 = 0
⇒ x = - 12, 6 (As x can't be negative)
⇒ x = 6
Present age of her sister = x = 6 years.
Present age of girl = 2x = 2(6) = 12 years.
Hence, the present age girl and her sister is 12 years and 6 years.
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