The average age of 3 sisters is 15. If the ages of 2 sisters are 12 years and 15 years, the age of the third sister is

Options

A. 21 years
B. 17 years
C. 18 years
D. 16 years

Answer

To find the age of the third sister, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Average Age**: We know that the average age of the three sisters is 15 years. The formula for average is:
\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of sisters}} \]
Here, the number of sisters is 3.

2. **Calculate the Total Age**: Since the average age is 15, we can find the total age of the three sisters by rearranging the formula:
\[ \text{Sum of ages} = \text{Average} \times \text{Number of sisters} \]
Therefore,
\[ \text{Sum of ages} = 15 \times 3 = 45 \text{ years} \]

3. **Identify the Ages of Two Sisters**: We are given the ages of two sisters:
- Age of Sister 1 (X) = 12 years
- Age of Sister 2 (Y) = 15 years

4. **Set Up the Equation for the Third Sister's Age**: Let the age of the third sister be Z. We can express the total age of the three sisters as:
\[ X + Y + Z = 45 \]
Substituting the known values:
\[ 12 + 15 + Z = 45 \]

5. **Solve for Z**: Combine the ages of the first two sisters:
\[ 27 + Z = 45 \]
Now, isolate Z by subtracting 27 from both sides:
\[ Z = 45 - 27 \]
\[ Z = 18 \]

6. **Conclusion**: The age of the third sister is 18 years.

### Final Answer:
The age of the third sister is **18 years**.