Respuesta :
I really want to say A, I mean all of these would fit for the one third of their ages but the two-fifths is kinda tricky. But I am sticking with A.
Answer:
Option: A is the correct answer.
A girl is 9; mom is 27
Step-by-step explanation:
A girl is now one-third as old as her mother.
i.e. if x is the present age of girl.
and y is the present age of her mother.
Then,
[tex]x=\dfrac{1}{3}y[/tex]
i.e.
[tex]y=3x-----------(1)[/tex]
In three years, she will be two-fifths as old as her mother will be.
This means after three years.
The age of girl will be: x+3
and the age of her mother will be: y+3
This means that:
[tex](x+3)=\dfrac{2}{5}\times (y+3)[/tex]
[tex]5(x+3)=2(y+3)\\\\i.e.\\\\5x+15=2y+6[/tex]
i.e.
[tex]5x+15=2\times 3x+6[/tex]
( since on using equation (1) )
i.e.
[tex]5x+15=6x+6\\\\i.e.\\\\6x-5x=15-6\\\\i.e.\\\\x=9[/tex]
and the value of y from equation (1) is:
[tex]y=27[/tex]
