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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. Find the age of the class teacher if the initial average was 14 years.
- a)35 years
- b)32 years
- c)29 years
- d)28 years
Correct answer is option 'C'. Can you explain this answer?
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The average age of a class of 30 students and a teacher reduces by 0....
Solution:
Given, the average age of a class of 30 students and a teacher is 14 years.
Let the age of the class teacher be x years.
Now, excluding the teacher, the average age of 30 students is (14 - x) years.
Again, it is given that if we exclude the teacher, the average age of the class reduces by 0.5 years.
Therefore, we can write:
14 - x = (total age of 30 students)/(number of students) - 0.5
14 - x = (total age of 30 students - 15)/(30 - 1)
14 - x = (total age of 30 students - 15)/29
Multiplying both sides by 29, we get:
406 - 29x = total age of 30 students - 15
total age of 30 students = 29x + 391
We know that the total age of 30 students and a teacher is:
30 * 14 + x = 420 + x
Also, we know that excluding the teacher, the total age of 30 students is:
29x + 391
Therefore, we can write:
29x + 391 = 420 + x - 0.5 * 30
Simplifying the above equation, we get:
29x + 391 = 405.5 + x
28x = 14.5
x = 0.5
Therefore, the age of the class teacher is:
x = 29 years
Hence, option (c) is the correct answer.
Given, the average age of a class of 30 students and a teacher is 14 years.
Let the age of the class teacher be x years.
Now, excluding the teacher, the average age of 30 students is (14 - x) years.
Again, it is given that if we exclude the teacher, the average age of the class reduces by 0.5 years.
Therefore, we can write:
14 - x = (total age of 30 students)/(number of students) - 0.5
14 - x = (total age of 30 students - 15)/(30 - 1)
14 - x = (total age of 30 students - 15)/29
Multiplying both sides by 29, we get:
406 - 29x = total age of 30 students - 15
total age of 30 students = 29x + 391
We know that the total age of 30 students and a teacher is:
30 * 14 + x = 420 + x
Also, we know that excluding the teacher, the total age of 30 students is:
29x + 391
Therefore, we can write:
29x + 391 = 420 + x - 0.5 * 30
Simplifying the above equation, we get:
29x + 391 = 405.5 + x
28x = 14.5
x = 0.5
Therefore, the age of the class teacher is:
x = 29 years
Hence, option (c) is the correct answer.
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Community Answer
The average age of a class of 30 students and a teacher reduces by 0....
The teacher after fulfilling the average of 14 (for the group to which he belonged) is also able to give 0.5 years to the age of each of the 30 students. Hence, he has 30x 0.5 = 15 years to give over and above maintaining his own average age of 14 years. Age of teacher = 14 + 30 x 0.5 = 29 years.
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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. Find the age of the class teacher if the initial average was 14 years.a)35 yearsb)32 yearsc)29 yearsd)28 yearsCorrect answer is option 'C'. Can you explain this answer?
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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. Find the age of the class teacher if the initial average was 14 years.a)35 yearsb)32 yearsc)29 yearsd)28 yearsCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. Find the age of the class teacher if the initial average was 14 years.a)35 yearsb)32 yearsc)29 yearsd)28 yearsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. Find the age of the class teacher if the initial average was 14 years.a)35 yearsb)32 yearsc)29 yearsd)28 yearsCorrect answer is option 'C'. Can you explain this answer?.
The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. Find the age of the class teacher if the initial average was 14 years.a)35 yearsb)32 yearsc)29 yearsd)28 yearsCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. Find the age of the class teacher if the initial average was 14 years.a)35 yearsb)32 yearsc)29 yearsd)28 yearsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average age of a class of 30 students and a teacher reduces by 0.5 years if we exclude the teacher. Find the age of the class teacher if the initial average was 14 years.a)35 yearsb)32 yearsc)29 yearsd)28 yearsCorrect answer is option 'C'. Can you explain this answer?.
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