# 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.

To find: Present ages

Method Used:

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic Equations51 mins
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Understand The Concept of Quadratic Equation45 mins
Quiz | Lets Solve Imp. Qs of Quadratic Equation43 mins
Balance the Chemical Equations49 mins
Champ Quiz | Quadratic Equation33 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses