The average age of a group of $15$ students is $10 \,years.$ When $5$ more students joined the group, the average got increased by $1\, year.$ The age of the new student is (in $years$)

$3 \,years$ ago the average age of a family of $5 \,members$ was $17 \,years,$ with the birth of a new baby, the average age of six members remains the same even today. Find the age of the new baby in $year$.

The mean of the marks obtained by $100$ students is $60 .$ If the marks obtained by one of the students was incorrectly calculated as $75$ whereas the actual marks obtained by him were $65,$ what is the correct mean of the marks obtained by the students?

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?

The average of $6$ numbers is $3.95.$ The average of two of them is $3.4,$ while the average of the other two is $3.85 .$ What is the average of the remaining two numbers ?

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