The average weight of $10$ students is increased by $0.5 \, kg$ when one of the students weighing $50 \, kg$ is replaced by a new student. Find the weight of the new student (in $kg$).

The average of certain first consecutive natural numbers is $20.5$. Find their sum.

The average age of three boys is $15$ years. If the ratio of their ages is $3:5:7$,what is the age of the oldest boy in years?

Of the three numbers, the second is twice the first and thrice the third. If the average of the three numbers is $44$, then the largest number 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

There were $35$ students in a hostel. If the number of students increases by $7$,the expenses of the mess increase by $Rs. 42$ per day,while the average expenditure per head diminishes by $Rs. 1$. Find the actual expenditure of the mess (in $Rs.$).