Final answer:
The problem is a ratio and proportion question where Samir's age is related to his father's and his sister Reema's age. We derive expressions in terms of Samir's age for all three individuals and compute the ratio of their ages to be 2:3:8.
Step-by-step explanation:
The question asked is a typical problem involving ratios and proportions in mathematics.
Let's denote the father's age as F, Samir's age as S, and Reema's age as R. According to the problem, Samir's age is one-fourth of his father's age and two-thirds of Reema's age. This gives us two relationships:
- S = \( \frac{1}{4} \)F
- S = \( \frac{2}{3} \)R
To find the ratio of Samir, Reema, and their father's ages, we need to express all ages in terms of one variable. Let's use Samir's age S as the reference.
Using the first relationship (S = \( \frac{1}{4} \)F), we can express the father's age as F = 4S.
Using the second relationship (S = \( \frac{2}{3} \)R), we can express Reema's age as R = \( \frac{3}{2} \)S.
So, the ratio of the ages of Samir, Reema, and their father is S : R : F which is equal to 1 : \( \frac{3}{2} \) : 4 or in whole numbers 2 : 3 : 8 after multiplying the entire ratio by 2 to clear the fraction.