Question

In a certain city there are $30$ colleges. Each college has $15$ peons, $6$ clerks, $1$ typist and $1$ section officer. The total number of posts of each kind in all the colleges is

Answer 1

Let $A=$Each college posts$=\left[\begin{array}{c}15\\ 6\\ 1\\ 1\end{array}\right]$
The total number of posts of each kind in all $30$ colleges is
$30A=30\left[\begin{array}{c}15\\ 6\\ 1\\ 1\end{array}\right]=\left[\begin{array}{c}450\\ 180\\ 30\\ 30\end{array}\right]$
Hence, the total number of posts of each kind in all the colleges$=450+180+30+30=690$