Final answer:
By setting up and solving algebraic equations based on the information provided, the present ages of the two people are found to be 14 years and 30 years respectively. So the correct answer is option B.
Step-by-step explanation:
The question asks to determine the present ages of two persons whose ages differ by 16 years and who had a 3-to-1 age ratio 6 years ago. To solve this, we employ algebraic methods, setting up equations based on the information given.
Step-by-Step Solution
- Let's assume the present age of the younger person is y years. Therefore, the present age of the elder person is y + 16 years, since their ages differ by 16 years.
- Six years ago, the younger person was y - 6 years old and the elder was (y + 16) - 6 or y + 10 years old.
- According to the problem, six years ago, the elder was 3 times as old as the younger. So, we can write the equation: 3(y - 6) = y + 10.
- Solving for y, we distribute the 3 into the parentheses to get 3y - 18 = y + 10. We then subtract y from both sides to get 2y - 18 = 10.
- Add 18 to both sides to get 2y = 28, and then divide by 2 to find y, which gives us y = 14. So, the current age of the younger person is 14 years.
- Adding 16 to the younger person's age, the current age of the elder person is 14 + 16 = 30 years.
Therefore, the present ages of the two persons are 14 years and 30 years.