A batsman has a certain average in $11$ innings. In the $12^{\text {th }}$ innings, he scores $90$ runs and his average decreases by $5 .$ After the $12^{\text {th }}$ innings what is his average?

The mean weight of $150$ students in a class is $60 \,kg.$ The mean weight of boys is $70\, kg$ and that of girls is $55 \,kg$. What is the number of boys in the class? 

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 decreases by $Rs.\, 1 .$ Find the original expenditure of the mess in $Rs.$

Out of nine persons, eight persons spent $Rs. \,30$ each for their meals. The ninth one spent $Rs. \,20$ more than the average expenditure of all the nine. The total money spent by all of them was (in $Rs.$)

In a class, there are $20$ boys whose average age is decreased by $2$ $months,$ when one boy aged $18\, years$ in replaced by a new boy. The age of the new boy is

Fifteen movie theatres average $600$ customers per theatre per day. If $six$ of the theaters close down but the total theater attendance stays the same, then the average daily attendance per theatre among the remaining theaters is