Question

The average age of 15 students is 18 years. If the teacher's age is added, the average increases by 1 year. What is the teacher's age?

• A. 32 years
• B. 34 years
• C. 35 years
• D. 33 years
• E. 30 years

Hint:

You can solve this mentally in seconds using the deviation method: The teacher must bring 18 years to maintain the old average, plus an extra 16 years (1 year for each of the 16 people now present) to raise the average by 1. So, \( 18 + 16 = 34 \).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given the initial average age of a group of students. When a new person (the teacher) joins the group, the overall average increases. We need to calculate the exact age of the teacher.


Step 2: Key Formula or Approach:
We rely on the fundamental property of averages:
\[ \text{Total Sum} = \text{Average} \times \text{Number of Items} \] The teacher's age is simply the difference between the new total age of the 16 individuals and the old total age of the 15 students.


Step 3: Detailed Explanation:
First, let's calculate the total sum of the ages of the 15 students:
\[ \text{Total age of students} = 15 \times 18 = 270 \text{ years} \] When the teacher is included, the total number of people in the group becomes \( 15 + 1 = 16 \).
The new average age increases by 1 year, making it \( 18 + 1 = 19 \text{ years} \).
Now, calculate the new total age of all 16 individuals:
\[ \text{Total age including teacher} = 16 \times 19 = 304 \text{ years} \] The teacher's exact age is the difference between these two totals:
\[ \text{Teacher's age} = 304 - 270 = 34 \text{ years} \]


Step 4: Final Answer:
The teacher's age is 34 years.