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The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. If the initial average is 14 years, find the age of the class teacher.
- a)27 years
- b)28 years
- c)29 years
- d)30 years
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The average age of a class of 30 students and a teacher reduces by 0.5...
Age of teacher = Total age(student + teacher) - total age of students
= 30 x 14 - 13 x 13.5
= 434 -403
= 29 years
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The average age of a class of 30 students and a teacher reduces by 0.5...
To solve this problem, we can use the concept of averages. Let's break down the given information and solve step by step:
Given:
- There are 30 students in the class.
- The average age of the class and the teacher is 14 years.
- If we exclude the teacher, the average age reduces by 0.5 years.
Step 1: Calculate the total age of the class and the teacher
Since the average age of the class and the teacher is 14 years, the total age of the class and the teacher can be calculated as follows:
Total age = Average age * Number of people
Total age = 14 * (30+1) [since there are 30 students and 1 teacher]
Total age = 14 * 31
Total age = 434
Step 2: Calculate the total age of the students
Since the average age reduces by 0.5 years when we exclude the teacher, the new average age becomes 14 - 0.5 = 13.5 years. Therefore, the total age of the students can be calculated as follows:
Total age of students = Average age of students * Number of students
Total age of students = 13.5 * 30
Total age of students = 405
Step 3: Find the age of the teacher
To find the age of the teacher, we subtract the total age of the students from the total age of the class and the teacher.
Age of the teacher = Total age - Total age of students
Age of the teacher = 434 - 405
Age of the teacher = 29
Therefore, the age of the class teacher is 29 years. Hence, the correct answer is option C.
Given:
- There are 30 students in the class.
- The average age of the class and the teacher is 14 years.
- If we exclude the teacher, the average age reduces by 0.5 years.
Step 1: Calculate the total age of the class and the teacher
Since the average age of the class and the teacher is 14 years, the total age of the class and the teacher can be calculated as follows:
Total age = Average age * Number of people
Total age = 14 * (30+1) [since there are 30 students and 1 teacher]
Total age = 14 * 31
Total age = 434
Step 2: Calculate the total age of the students
Since the average age reduces by 0.5 years when we exclude the teacher, the new average age becomes 14 - 0.5 = 13.5 years. Therefore, the total age of the students can be calculated as follows:
Total age of students = Average age of students * Number of students
Total age of students = 13.5 * 30
Total age of students = 405
Step 3: Find the age of the teacher
To find the age of the teacher, we subtract the total age of the students from the total age of the class and the teacher.
Age of the teacher = Total age - Total age of students
Age of the teacher = 434 - 405
Age of the teacher = 29
Therefore, the age of the class teacher is 29 years. Hence, the correct answer is option C.
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The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. If the initial average is 14 years, find the age of the class teacher.a)27 yearsb)28 yearsc)29 yearsd)30 yearsCorrect answer is option 'C'. Can you explain this answer?
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