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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

User Kevin Kopf
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2 Answers

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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.
User Shyam S
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Answer:

Option: A is the correct answer.

A girl is 9; mom is 27

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=(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)=(2)/(5)* (y+3)


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

i.e.


5x+15=2* 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

User Anurag Soni
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