The average salary of all the staff in an office of a corporate house is $Rs. 5,000$. The average salary of the officers is $Rs. 14,000$ and that of the rest is $Rs. 4,000$. If the total number of staff is $500$,what is the number of officers?

The average marks obtained by a class of $60$ students is $65$. The average marks of half of the students is found to be $85$. The average marks of the remaining students is:

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 age of $10$ men is increased by $2 \, \text{years}$ when one of them, aged $25 \, \text{years}$, is replaced by a new man. What is the age of the new man (in $\text{years}$)?

In a competitive examination,the average marks obtained was $45$. It was later discovered that there was some error in computerization and the marks of $90$ candidates had to be changed from $80$ to $50$,and the average came down to $40$ marks. The total number of candidates appeared in the examination is

The sum of five consecutive integers is $a$ and the sum of the next five consecutive integers is $b$. Then $\frac{(b-a)}{100}$ is equal to