Q. 195.0( 4 Votes )

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

Answer :

To find: Present ages


Method Used:


To solve the quadratic equation by factorisation method, follow the steps:


1) Multiply the coefficient of x2 and constant term.


2) factorise the result obtained in step 1.


3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them


You get coefficient of x.


Explanation:


Let the present ages of the younger sister be ‘a’.


Given, girl is twice as old as her sister.


Age of elder sister = 2a


Also, four years ago, the product of their ages (in years) will be 160.


(a + 4) (2a + 4) = 160


2a2 + 12a + 16 – 160 = 0


2a2 + 12a – 144 = 0


a2 + 6a – 72 = 0


Split the middle term.


a2 + 12a – 6a – 72 = 0


a (a + 12) – 6(a + 12) = 0


(a – 6) (a + 12) = 0


a = 6 and a =-12


As age cannot be negative,


a = 6 years


So 2a = 2(6) = 12 years


Hence age of sisters is 6 years and 12 years.


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