Answer:
Option B - father's age = 52; daughter's age = 13
Step-by-step explanation:
Given : A girl is now one-fourth as old as her father, and in seven years, she will be one-half as old as her father was twelve years ago.
To find : What are her and her father's present ages?
Solution :
Let the father's present age is 'x'.
A girl is now one-fourth as old as her father.
i.e. Girl age is [tex]\frac{x}{4}[/tex]
In seven years, she will be one-half as old as her father was twelve years ago.
i.e. [tex]\frac{x}{4}+7=\frac{1}{2}(x-12)[/tex]
[tex]\frac{x}{4}+7=\frac{x}{2}-6[/tex]
[tex]\frac{x}{4}-\frac{x}{2}=-6-7[/tex]
[tex]\frac{x-2x}{4}=-13[/tex]
[tex]-x=-52[/tex]
[tex]x=52[/tex]
The father's age is 52 years.
The daughter's age is [tex]\frac{52}{4}=13[/tex]
Therefore, option B is correct.
