In a cricket team of $11$ boys,one player weighing $42 \,kg$ is injured and replaced by another player. If the average weight of the team is increased by $100 \,g$ as a result of this,then what is the weight of the new player (in $.1$)? (in $kg$)

The average of $13$ results is $50$. If the average of the first $7$ results is $52$ and that of the last $7$ results is $49$,find the $7^{th}$ result.

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)?

The average annual income (in $Rs.$) of certain agricultural workers is $S$ and that of other workers is $T$. The number of agricultural workers is $11$ times that of other workers. Then the average annual income (in $Rs.$) of all the workers is

The sum of the ages of father and son at present is $33 \, \text{years}$. Two years ago, the product of their ages was $28 \, \text{years}$. What is the age of the father and the son (in $\text{years}$)?

$A$ cricketer had a certain average of runs for his $64$ innings. In his $65^{th}$ innings,he is bowled out for no score on his part. This brings down his average by $2$ runs. What is his new average of runs?