Average age of A and B is 20 years. B and C is 18 years. A and C is 21 years. What is the average age (in years) of A, B and C?

Options

A. 7.1
B. 19.67
C. 19
D. 29.5

Answer

To find the average age of A, B, and C, we can follow these steps:

1. **Set up the equations based on the given averages**:
- From the average age of A and B being 20 years:
\[ \frac{A + B}{2} = 20 \implies A + B = 40 \quad \text{(Equation 1)} \]
- From the average age of B and C being 18 years:
\[ \frac{B + C}{2} = 18 \implies B + C = 36 \quad \text{(Equation 2)} \]
- From the average age of A and C being 21 years:
\[ \frac{A + C}{2} = 21 \implies A + C = 42 \quad \text{(Equation 3)} \]

2. **Add all three equations together**:
\[ (A + B) + (B + C) + (A + C) = 40 + 36 + 42 \]
This simplifies to:
\[ 2A + 2B + 2C = 118 \]

3. **Divide the entire equation by 2**:
\[ A + B + C = \frac{118}{2} = 59 \]

4. **Calculate the average age of A, B, and C**:
\[ \text{Average age} = \frac{A + B + C}{3} = \frac{59}{3} \approx 19.67 \]

Thus, the average age of A, B, and C is approximately **19.67 years**.