Question

27. The age of a boy is double the age of his brother. After 4 years product of their ages will be
160. Find their present ages.​

Answer 1

Step-by-step explanation:

Let the age of the boy = x

Let the age of his brother = y

According to the given question,

x=2(y)

and,

after 4 years

the ages will be

(x+4), (y+4)

So, the product of their ages will be

(x+4).(y+4)=160

=> xy +4x +4y +16 = 160

=> xy + 8y +4y +16 =160

=> xy +12y = 144

=> y(x+12)=144

=>y(2y+12)=144

=> 2y2 +12y-144=0

=> 2y2-24y+12y-144=0

=> 2y(y-12)+12(y-12)=0

=> (2y+12)(y-12)=0

=> y=12, since age cannot be negative.

so, boys age = 12 years

brothers age = 24 years