Final answer:
To find Rina and her younger sister's present ages, we can use algebraic equations and solve them step-by-step. Rina's present age is 18 years and her younger sister's present age is 12 years.
Step-by-step explanation:
To solve this problem, we can use algebra. Let's start by defining variables for the present ages of Rina and her younger sister. Let's say Rina's present age is x years, and her younger sister's present age is y years.
According to the problem, Rina is 6 years older than her younger sister, so we can write the equation: x = y + 6.
After 10 years, Rina's age will be x + 10 and her younger sister's age will be y + 10. The problem states that the sum of their ages will be 50 years, so we can write the equation: (x + 10) + (y + 10) = 50.
Now we can solve these two equations to find the present ages of Rina and her younger sister. Substituting x = y + 6 from the first equation into the second equation, we get (y + 6 + 10) + (y + 10) = 50. Simplifying this equation, we get 2y + 26 = 50. Subtracting 26 from both sides, we get 2y = 24. Dividing both sides by 2, we get y = 12. Substituting y = 12 into the first equation, we get x = 12 + 6 = 18.
Therefore, Rina's present age is 18 years and her younger sister's present age is 12 years.