$A$ cricketer gives $12.4$ runs per wicket. He gives $26$ runs and takes $5$ wickets in a match,after which his average becomes $12$ runs per wicket. How many wickets had been taken till the last match?

$A$ man spends $Rs. 1800$ monthly on an average for the first four months and $Rs. 2000$ monthly for the next eight months and saves $Rs. 5600$ a year. His average monthly income is (in $Rs.$)

The average weight of three boys $A, B$ and $C$ is $54 \frac{1}{3} \, kg,$ while the average weight of three boys $B, D$ and $E$ is $53 \, kg.$ What is the average weight of $A, B, C, D$ and $E$ (in $kg$)?

The average of the two-digit numbers,which remain the same when the digits interchange their position,is:

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 $Rs$.

In a set of prime and composite numbers,the number of composite numbers is twice the number of prime numbers,and the average of all the numbers in the set is $9$. If the number of prime numbers and composite numbers are exchanged,then the average of the set of numbers increases by $2$. If,during the exchange of the numbers,the average of the prime numbers and composite numbers individually remained constant,then what was the ratio of the average of composite numbers to the average of prime numbers (initially)?