Question

The average age of 30 students in a group is 18 years. When the teacher's age is included, the average age of the group increases by 1 year. What is the teacher's age (in years)?

• A. 49
• B. 56
• C. 40
• D. 45

Answer 1

Answer:

A. 49

Step 1: Total age of 30 students

Average age of 30 students = 18 years

$\text{Total age of 30 students} = 30 \times 18 = 540 \text{ years}$

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Step 2: Average when teacher is included

Number of people = 30 students + 1 teacher = 31

New average = 18 + 1 = 19 years

$\text{Total age including teacher} = 31 \times 19 = 589 \text{ years}$

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Step 3: Teacher’s age

$\text{Teacher’s age} = \text{Total with teacher} - \text{Total of students} = 589 - 540 = 49$

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Teacher’s age = 49 years