A batch of $60$ students made an average score of $50$ marks and another batch of $40$ students made it only $45 .$ What is the overall average score ?

The average weight of $8$ persons increases by $2.5\, kg$ when a new person comes in place of one of them weighing $65\, kg$. What might be the weight of the new person? (in $kg$)

The average age of Donald, his wife and their two children is $23\, years.$ His wife is just $4 \,year$ younger than Donald himself andxhis wife was $24\, years$ old when his daughter was born. He was $32 \,years$ old when his son was born. Th average age of Donald and his daughter is ? (in $year$)

The average age of $24$ boys and their teacher is $15 \,years.$ When the teacher's age is excluded, the average age decreases by $1\, year.$ The age of the teacher is in $years$ ?

The average age of $80$ boys in a class is $15.$ The average age of a group of $15$ boys in the class is $16$ and the average age of another $25$ boys in the class is $14 .$ What is the average age of the remaining boys in the class ?

If the average of $m$ numbers is $n^{2}$ and that of $n$ numbers is $m^{2}$, then the average of $( m + n )$ numbers is