The average age of 14 girls and their teacher's age is 15 years. If the teacher's age is excluded, the average re duces by 1. What is the teacher's age?

Options

A. 35 years
B. 32 years
C. 30 years
D. 29 years

Answer

To find the teacher's age based on the given information, we can follow these steps:

### Step 1: Calculate the total age of 14 girls and the teacher
The average age of 14 girls and their teacher is given as 15 years. Therefore, we can calculate the total age of the 14 girls and the teacher using the formula for average:

\[ \text{Total Age} = \text{Average Age} \times \text{Number of Individuals} \]

Here, the number of individuals is 14 girls + 1 teacher = 15.

\[ \text{Total Age} = 15 \times 15 = 225 \text{ years} \]

### Step 2: Calculate the new average age without the teacher
When the teacher's age is excluded, the average age of the 14 girls decreases by 1 year, making the new average age 14 years.

### Step 3: Calculate the total age of the 14 girls
Using the new average age, we can calculate the total age of the 14 girls:

\[ \text{Total Age of 14 Girls} = \text{New Average Age} \times \text{Number of Girls} \]

\[ \text{Total Age of 14 Girls} = 14 \times 14 = 196 \text{ years} \]

### Step 4: Calculate the teacher's age
Now that we have the total age of the 14 girls and the total age of the 14 girls and the teacher, we can find the teacher's age by subtracting the total age of the girls from the total age of the group:

\[ \text{Teacher's Age} = \text{Total Age} - \text{Total Age of 14 Girls} \]

\[ \text{Teacher's Age} = 225 - 196 = 29 \text{ years} \]

### Conclusion
The teacher's age is 29 years.

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