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

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 $\frac{x}{4}$

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

i.e. $\frac{x}{4}+7=\frac{1}{2}(x-12)$

$\frac{x}{4}+7=\frac{x}{2}-6$

$\frac{x}{4}-\frac{x}{2}=-6-7$

$\frac{x-2x}{4}=-13$

$-x=-52$

$x=52$

The father's age is 52 years.

The daughter's age is $\frac{52}{4}=13$

Therefore, option B is correct.