The mean of $11$ numbers is $35$. If the mean of the first $6$ numbers is $32$ and that of the last $6$ numbers is $37$, then find the sixth number.

The average of $7$ consecutive numbers is $20$. The largest of these numbers is

The average of five numbers is $6.9$. If one of the numbers is deleted,the average of the remaining numbers is $4.4$. What is the value of the number deleted?

There was one mess for $30$ boarders in a certain hostel. On the number of boarders being increased by $10,$ the expenses of the mess were increased by $Rs.\, 40$ per month while the average expenditure per head diminished by $Rs.\, 2.$ Find out the actual monthly expenses (in $Rs.$).

The average of $6$ observations is $12$. $A$ new seventh observation is included and the new average is decreased by $1$. The seventh observation is

The average age of a group of $18$ persons is $32$ $years$ and $6$ $months$. If two persons of age $65$ $years$ each and one person of age $50$ $years$ leave the group,the average age of the remaining persons in the group will be (in $years$)