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The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
- a)48
- b)45
- c)43
- d)44
- e)46
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The average age of a class of 22 students is 21 years. The average inc...
Total age of all students
= 22 × 21
= 22 × 21
Total age of all students + Age of the teacher = 23 × 22
Most Upvoted Answer
The average age of a class of 22 students is 21 years. The average inc...
Given:
- The average age of a class of 22 students is 21 years.
- The average increased by 1 when the teacher's age is included.
To find:
- The age of the teacher.
Solution:
Let's assume the age of the teacher is 'x' years.
Average age of the class:
The average age of the class can be calculated by summing up the ages of all the students and dividing it by the total number of students.
Average age = (Sum of ages of all students) / (Total number of students)
Given that the average age of the class is 21 years, we can write the equation as:
21 = (Sum of ages of all students) / 22
Average age with the teacher:
When the teacher's age is included, the total number of people in the class becomes 23 (22 students + 1 teacher). The average age increases by 1.
New average age = 21 + 1 = 22
The sum of ages of all the students and the teacher can be calculated using the new average age and the total number of people in the class.
Sum of ages of all students and teacher = New average age * Total number of people
Sum of ages of all students and teacher = 22 * 23
Equation:
Now, we can set up an equation using the sum of ages of all the students and the teacher.
(Sum of ages of all students and teacher) = (Sum of ages of all students) + (Age of the teacher)
22 * 23 = 21 * 22 + x
506 = 462 + x
x = 506 - 462
x = 44
Therefore, the age of the teacher is 44 years. Option D is the correct answer.
- The average age of a class of 22 students is 21 years.
- The average increased by 1 when the teacher's age is included.
To find:
- The age of the teacher.
Solution:
Let's assume the age of the teacher is 'x' years.
Average age of the class:
The average age of the class can be calculated by summing up the ages of all the students and dividing it by the total number of students.
Average age = (Sum of ages of all students) / (Total number of students)
Given that the average age of the class is 21 years, we can write the equation as:
21 = (Sum of ages of all students) / 22
Average age with the teacher:
When the teacher's age is included, the total number of people in the class becomes 23 (22 students + 1 teacher). The average age increases by 1.
New average age = 21 + 1 = 22
The sum of ages of all the students and the teacher can be calculated using the new average age and the total number of people in the class.
Sum of ages of all students and teacher = New average age * Total number of people
Sum of ages of all students and teacher = 22 * 23
Equation:
Now, we can set up an equation using the sum of ages of all the students and the teacher.
(Sum of ages of all students and teacher) = (Sum of ages of all students) + (Age of the teacher)
22 * 23 = 21 * 22 + x
506 = 462 + x
x = 506 - 462
x = 44
Therefore, the age of the teacher is 44 years. Option D is the correct answer.
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The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?a)48b)45c)43d)44e)46Correct answer is option 'D'. Can you explain this answer?
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The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?a)48b)45c)43d)44e)46Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?a)48b)45c)43d)44e)46Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average age of a class of 22 students is 21 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?a)48b)45c)43d)44e)46Correct answer is option 'D'. Can you explain this answer?.
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