The average of the test scores of a class of $m$ students is $70$ and that of $n$ students is $91$. When the scores of both the classes are combined,the average is $80$. What is $n / m$?

The average monthly expenditure of a family for the first four months is $Rs. 2750$,for the next three months is $Rs. 2940$,and for the last five months is $Rs. 3130$. If the family saves $Rs. 5330$ throughout the year,find the average monthly income of the family for that year (in $Rs.$).

Eleven years earlier,the average age of a family of $4$ members was $28 \, \text{years}$. Now,the average age of the same family with $6$ members is still the same,even though $2$ children were born in this period. If they belong to the same parents and the age of the first child at the time of the birth of the younger child was the same as the total number of family members just after the birth of the youngest member,then what is the present age of the youngest member of the family in years?

The average salary of all the associates in a team is $Rs. 16000$. The average salary of $7$ senior associates is $Rs. 24000$ and the average salary of the rest is $Rs. 12000$. How many associates work in that team?

Five years ago,the average age of $P$ and $Q$ was $15 \text{ years}$. Now,the average age of $P$,$Q$,and $R$ is $20 \text{ years}$. What will be the age of $R$ after $10 \text{ years}$?

$A$ batsman makes a score of $270$ runs in the $87^{th}$ inning and thus increases his average by a certain number of runs that is a whole number. Find the possible values of the new average.