Question

Q.4) The ratio between the present age of a girl!
and her grandfather is 2 : 23, and the present
age of the father of the girl is half of the age of
her grandfather. The ratio between the present
age of the mother and father of the girl is 19: 23,
and the difference between the present age of
the girl and her mother is 30. Then what is the
total age of the girl and her father?​

Answer 1

Answer:

54 years.

Step-by-step explanation:

Let the present age of girl and the grandfather be x years and y years.

As per the question,

The ratio between the present age of a girl and her grandfather is 2 : 23. So, we have $\frac{x}{y}=\frac{2}{23}$ ...(1)

Now, it is given that the present age of the father is half of the grandfather.

So, the age of father will be $\frac{y}{2}$.

Let the present age of mother be z yrs.

Also, it is given that the ratio between the present  age of the mother and father of the girl is 19: 23.

So, we have

$\frac{z}{\frac{y}{2} } =\frac{19}{23}$

$\implies\frac{2z}{y} =\frac{19}{23}$

$\implies z=\frac{19}{46}y$ ...(2)

Now, it is given that he difference between the present age of

the girl and her mother is 30.

So, we have

$z-x=30$

$z-x=30$

$\implies\frac{19y}{46} -\frac{2y}{23} =30$  [Using (1) and (2)]

$\implies\frac{19y-4y}{46} =30$

$\implies\frac{15y}{46} =30$

$\implies y=92$

So, the present age of the grandfather is 92 years.

Present age of father is $\frac{92}{2}=46$ years.

Present age of girl is $\frac{2}{23} \times92=8$ years.

Therefore, the total age of the girl and her father is $46+8=54$ years.