The average of $n$ numbers $x_{1}, x_{2}, \ldots, x_{n}$ is $\bar{x}$. Then,the value of $\sum_{i=1}^{n}(x_{i}-\bar{x})$ is equal to

Out of four numbers,whose average is $60$,the first one is one-fourth of the sum of the last three. The first number is

$A, B, C$ and $D$ are four consecutive odd numbers and their average is $42$. What is the product of $B$ and $D$?

Three years ago,the average age of a family of $5$ members was $27 \text{ years}$. After the addition of a child to the family,the present average age of the family is still $27 \text{ years}$. Find the present age of the child (in years).

The average weight of $8$ persons increases by $2.5\, kg$ when a new person comes in place of one of them weighing $65\, kg$. What is the weight of the new person? (in $kg$)

The average salary,per head,of all the workers of an institution is $Rs.\, 60$. The average salary of $12$ officers is $Rs.\, 400$; the average salary,per head,of the rest is $Rs.\, 56$. The total number of workers in the institution is: