Final answer:
Using a system of equations, the present age of the elder person is found to be 30 years. The ages of the two persons differ by 16 years, and 6 years ago, the elder was three times as old as the younger.
Step-by-step explanation:
To solve the problem, let's denote the present age of the younger person as y and the present age of the elder person as e. We know that the ages differ by 16 years, and 6 years ago, the elder one was 3 times as old as the younger one. Based on these facts, we can establish two equations:
- e = y + 16 (the elder is 16 years older)
- e - 6 = 3(y - 6) (6 years ago, the elder was 3 times as old)
Substitute the first equation into the second one:
- (y + 16) - 6 = 3(y - 6)
- y + 10 = 3y - 18
- 28 = 2y
- y = 14
Once we have the age of the younger person, we can find the age of the elder person:
- e = y + 16 = 14 + 16 = 30
The present age of the elder person is 30 years.
Thus, the correct answer is (b) 30.