How old will C be after 10 years ?
(i) Five years ago, the average age of A and B was 15 years.
(ii) Average ages of A,B and C today is 20 years.

Answer

To solve the question "How old will C be after 10 years?", we will analyze the provided statements step by step.

### Step 1: Analyze the first statement
The first statement tells us that five years ago, the average age of A and B was 15 years.

- **Calculation**:
- If the average age of A and B five years ago was 15 years, then the total age of A and B five years ago can be calculated as:
\[ \text{Total age of A and B five years ago} = 15 \times 2 = 30 \text{ years} \]
- Therefore, the total age of A and B today (adding 5 years for each) is:
\[ \text{Total age of A and B today} = 30 + 5 + 5 = 40 \text{ years} \]

### Step 2: Analyze the second statement
The second statement states that the average age of A, B, and C today is 20 years.

- **Calculation**:
- The total age of A, B, and C today can be calculated as:
\[ \text{Total age of A, B, and C today} = 20 \times 3 = 60 \text{ years} \]

### Step 3: Set up equations
Now we have two equations:
1. Total age of A and B today: \( A + B = 40 \) years (from Step 1)
2. Total age of A, B, and C today: \( A + B + C = 60 \) years (from Step 2)

### Step 4: Find C's age
To find C's age, we can subtract the first equation from the second:
\[ (A + B + C) - (A + B) = 60 - 40 \]
This simplifies to:
\[ C = 20 \text{ years} \]

### Step 5: Calculate C's age after 10 years
Now that we know C's current age, we can find out how old C will be after 10 years:
\[ C's \text{ age after 10 years} = C's \text{ current age} + 10 = 20 + 10 = 30 \text{ years} \]

### Final Answer
C will be 30 years old after 10 years.

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