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- Standard 13
- Quantitative Aptitude
The average age of board of directors of a company, having $10$ directors was $48$ years. Coincidentally when a director aged $53$ resigned from the board of directors, another director died on the same day. So a new director joined the board of directors aged $34.$ Next year in the same month the average age of all the $9$ directors was found to be $46 \,years.$ The age of the late (i.e., dead) director at the time of his death was (in $years$)
$56$
$53$
$57$
$61$
Solution
$\begin{array}{|l|c|c|c|} \hline & \begin{array}{c} \text { No of } \\ \text { Directors } \end{array} & \begin{array}{c} \text { Average } \\ \text { Age } \end{array} & \text { Total age } \\ \hline \text { Just before } & & & \\ \begin{array}{l} \text { death and } \\ \text { resignation } \end{array} & 10 & 48 & 480 \\ \hline \begin{array}{l} \text { Just after } \\ \text { death and } \\ \text { resignation } \end{array} & 9 & & \begin{array}{c} (480-(53+ x ) \\ +34 \end{array} \\ \hline \text { one year later } & 9 & 46 & 414 \\ \hline \end{array}$
So one year later, after the incident total age $=\{480-(53+x)+34\}+9 \times 1=414 \quad x=56$
where $x$ is the age of the dead person at the time of his death.
