The average of $20$ numbers is $30$ and that of other $30$ numbers is $50$. What is the average of all the numbers?

There were $35$ students in a hostel. If the number of students is increased by $7$,the expenditure on food increases by $Rs. \,42$ per day,while the average expenditure per student is reduced by $Rs. \,1$. What was the initial total expenditure on food per day? (in $Rs.$)

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 $Rs$.

Of the three numbers,the first is twice the second and the second is thrice the third. If the average of the three numbers is $10$,the numbers are

The average of $50$ numbers is $38$. If two numbers,namely,$45$ and $55$ are discarded,what is the average of the remaining numbers (in $.5$)?

$A$ 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?