Question

A girl is now one-third as old as her mother. In three years, she will be two-fifths as old as her mother will be. What are their present ages?
A girl is 9; mom is 27
B girl is 18; mom is 54
C girl is 25; mom is 75

Answer 1

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,

$x=\dfrac{1}{3}y$

i.e.

$y=3x-----------(1)$

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:

$(x+3)=\dfrac{2}{5}\times (y+3)$

$5(x+3)=2(y+3)\\\\i.e.\\\\5x+15=2y+6$

i.e.

$5x+15=2\times 3x+6$

( since on using equation (1) )

i.e.

$5x+15=6x+6\\\\i.e.\\\\6x-5x=15-6\\\\i.e.\\\\x=9$

and the value of y from equation (1) is:

$y=27$

Answer 2

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.