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- Standard 13
- Quantitative Aptitude
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.
Both $I$ and $III$
Both $I$ and $II$
$II$ and either $I$ or $III$
All $I,$ $II$ and $III$
Solution
From $I.$ There are $11$ students in the class.
From $II.$ The average age of students and class teacher is $14$ years.
From $III.$ The average age of class teacher is $3$ years more than that of students.
Now, combining all three statements,
we have Average age of (students $+$ teacher) $=14 \times 12=168$ years
Average age of $11$ students $=14-3=11$ years
Total age of $11$ students $=11 \times 11=121$ years
Teacher's age $=168-121=47$ years.
