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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. What are her and her father's present ages?A. father's age = 20; daughter's age = 5B. father's age = 52; daughter's age = 13C. father's age = 76; daughter's age = 19

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Answer:

Option B - father's age = 52; daughter's age = 13

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
(x)/(4)

In seven years, she will be one-half as old as her father was twelve years ago.

i.e.
(x)/(4)+7=(1)/(2)(x-12)


(x)/(4)+7=(x)/(2)-6


(x)/(4)-(x)/(2)=-6-7


(x-2x)/(4)=-13


-x=-52


x=52

The father's age is 52 years.

The daughter's age is
(52)/(4)=13

Therefore, option B is correct.

User Dule Arnaux
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