Question

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

Answer 1

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.