Question

Six year before, the age of mother was equal to the square of her son's

age. Three year hence, her age will be thrice the age of her son then.

Find the present ages of the mother and son?

Answer 1

hey ...

Let the present age of mother be x yrs and son be y yrs .
6 yr before ,
the age of son = (y - 6) yrs
the age of mother = ( x - 6 ) yrs
then,
accor. to the que .....
(x-6) = (y-6)^2
= x-6 = y^2 - 36 - 12y
= x -6 + 36 = y^2 -12y
= x + 30 = y^2 -12 y
= x = y^2 - 12y - 30 --------(i)

3 year hence ,
the age of mother = 3 + x
the age of son = 3 + y
accor. to the que .....
3 + x = 3(3 + y)
3 + x = 9 + 3y
x + 3 - 9 - 3y = 0
x - 3y - 6 = 0 --------(ii)

now , putting eq (i) in eq (ii)
y^2 - 12y - 30 - 3y - 6 = 0
y^2 - 15y + 36= 0
y^2 -12y - 3y + 36 =0
( y^2 - 12 y ) (- 3 y + 36 ) =0
y ( y -12 ) - 3 ( y - 12 ) =0
(y - 3 ) ( y - 12 ) =0
y = 12

the present age of son = 12 yrs
now , putting y = 12 in eq (ii)
x - 3y - 6 = 0
x - 3 (12) - 6 = 0
x - 36 - 6 = 0
x = 42

the present age of mother = 42 yrs .


hope this will help uh ....
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