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- Quantitative Aptitude
$10$ $years$ ago the average age of all the $25$ $teachers$ of the Girls college was $45\, years.$ $4 \,years$ ago, the principal has retired from her post at the age of $60 \,year.$ So after one year a new principal whose age was $54 \,years$ recruited from outside. The present average age of all the teachers is, if principal is also considered as a teacher
Solution
$10$ years ago average age of $25$ teachers $=45$ years
$4 \,years$ ago (just before the retirement of principal) avẹrage age of $25$ teachers $=45+6=51$
and at the same time total age of $25$ teachers $=51 \times 25=8275$
and the total age of remaining $24$ teachers when just principal. has retired $=1275-60=1215$ years
$1$ year later (i.e. $3 \,years$ ago from present)
total age of $25$ teacher (just before the recruitment of new principal) $=1215+(1 \times 24)=1239$ years.
and the total age of $24$ teacher including new principal just after the recuitment $=1239+54=1293$ years.
Thus the present age of all the $25$ teachers
$=1293+3 \times 25=1368 \text { years. }$
Hence the present average age of the $25$ teacher.
$=\frac{1368}{25}=54 \frac{18}{25} \text { years }$
