What is the age of a class teacher?I. There a | vedclass

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(D) Let the number of students be $n = 11$ (from statement $I$).Let the average age of the students be $A_s$ and the age of the teacher be $T$.From st

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All $I, II$ and $III$

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(D) Let the number of students be $n = 11$ (from statement $I$).Let the average age of the students be $A_s$ and the age of the teacher be $T$.From statement $II$,the average age of $11$ students and the teacher is $14$ years:$\frac{11 	imes A_s + T}{12} = 14 \implies 11A_s + T = 168$ (Equation $1$).From statement $III$,the average age of the teacher and the students is $3$ years more than the average age of the students:$\frac{11A_s + T}{12} = A_s + 3$.Since $\frac{11A_s + T}{12} = 14$ from statement $II$,we have $14 = A_s + 3$,which gives $A_s = 11$ years.Substituting $A_s = 11$ into Equation $1$:$11(11) + T = 168$$121 + T = 168$$T = 168 - 121 = 47$ years.Thus,all three statements $I, II,$ and $III$ are required to find the teacher's age.

What is the age of a class teacher?
$I.$ There are $11$ students in the class.
$II.$ The average age of the students and the teacher is $14$ years.
$III.$ The average age of the teacher and the students is $3$ years more than that of the students.

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What is the age of a class teacher?$I.$ There are $11$ students in the class.$II.$ The average age of the students and the teacher is $14$ years.$III.$ The average age of the teacher and the students is $3$ years more than that of the students.