The average age of a class of 30 students and | vedclass

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Question

(A) Let the number of students be $30$ and the teacher be $1$. Total number of people $= 30 + 1 = 31$.Initial average age of $31$ people $= 14 \, 	ex

Vedclass · Accepted Answer

$29$

Vedclass · Answer

(A) Let the number of students be $30$ and the teacher be $1$. Total number of people $= 30 + 1 = 31$.Initial average age of $31$ people $= 14 \, 	ext{years}$.Total age of $31$ people $= 31 	imes 14 = 434 \, 	ext{years}$.When the teacher is excluded,the number of students remains $30$.The new average age reduces by $0.5 \, 	ext{years}$,so the new average $= 14 - 0.5 = 13.5 \, 	ext{years}$.Total age of $30$ students $= 30 	imes 13.5 = 405 \, 	ext{years}$.Age of the teacher $= (	ext{Total age of } 31 	ext{ people}) - (	ext{Total age of } 30 	ext{ students})$.Age of the teacher $= 434 - 405 = 29 \, 	ext{years}$.

The average age of a class of $30$ students and a teacher reduces by $0.5 \, \text{years}$ if we exclude the teacher. If the initial average is $14 \, \text{years}$,find the age of the class teacher in $\text{years}$.

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