The average weight of $100$ students is $32\, kg$. The average weight of first $49$ students is $30\, kg$ and that of last $50$ students is $34\, kg$. What is the weight (in $kg$ ) of the $50^{ th }$ student ?

The average of $X_{1}, X_{2}$ and $X_{3}$ is $14 .$ Twice the sum of $X_{2}$ and $X_{3}$ is $30 .$ What is the value of $X_{1} ?$

Average age of $A, B$ and $C$ is $84\, years.$ When $D$ joins them the average age becomes $80\, years.$ A new person, $E,$ whose age is $4 \,years$ more than $D,$ replaces $A$ and the average of $B, C, D$ and $E$ becomes $78\, years.$ What is the age of $A$ ? (in $years$)

The average salary per head of all the workers in a company is $Rs. \,95.$ The average salary of $15$ officers is $Rs.\, 525$ and the average salary per head of the rest is $Rs. \,85.$ Find the total number of workers in the workshop.

The average salary of all the workers in a workshop is $Rs.\,8000.$ The average salary of $7$ technicians is $Rs.\, 12000$ and the average salary of the rest is $Rs.\,6000 .$ The total number of workers in the workshop is