Final answer:
To find person C's present age, we use the given average and the sum of A and B's ages from two years ago to derive equations. Solving these equations reveals that person C's current age is 31 years, which is not among the provided options.
Step-by-step explanation:
The question asks us to find the present age of person C, given the average age of A, B, and C is 20 years, and two years ago, the sum of the ages of A and B was 6 years more than that of C.
First, let's calculate the total present age of A, B, and C using the average age:
- The average age of A, B, and C is 20 years. Therefore, the total present age for A, B, and C combined is 20 years * 3 people = 60 years.
- Two years ago, the sum of the ages of A and B (let's call this sum 'S') was 6 more than that of C. So, S + C - 2 (this '-2' accounts for C's age two years ago) = 60 years.
- Two years ago, A and B's combined age would be S - 4 (since each was two years younger) and C's age would be C - 2.
- So, S - 4 = (C - 2) + 6, simplifying this, we get S = C + 4.
- Replacing S in the second point with C + 4, we get (C + 4) + (C - 2) = 60 years, which simplifies to 2C + 2 = 60.
- Solving for C, we have 2C = 58, so C = 29 years.
However, since we are looking for the present age, we need to add two years back to 29 since we previously subtracted them to find C's age two years ago. Therefore, C's present age is 29 + 2 = 31 years. Therefore, none of the options provided (16 years, 18 years, 20 years, 22 years) are correct; the correct present age for C is 31 years.