Daughter's age is one-fourth of her father's age. Five years hence, she will be one-third of his age. Further after five years, what will be the ratio of her age to that of her father?

Correct option is C

Given:

Let the daughter's current age be D and the father's current age be F .

It is given that: D = $$\frac{F}{4}$$​.

Also, five years hence, the daughter's age will be  D + 5 , and the father's age will be  F + 5 .

At that time, the daughter's age will be one-third of the father's age, i.e., $$D + 5 = \frac{F + 5}{3}$$​​

Solution:

From the two given conditions, we solve the system of equations to find the current ages of the daughter and father:

Current age of daughter: 10 years

Current age of father:  40  years} 

After 10 years (5 + 5), the daughter will be  20 years old, and the father will be 50  years old.

Thus, the ratio of the daughter's age to the father's age after 10 years will be:

​$$\frac{20}{50} = \frac{2}{5}$$​​

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