The mean weight of $34$ students of a school is $42\, kg$. If the weight of the teacher be included, the mean rises by $400\, g.$ Find the weight (in $kg$) of the teacher.

Out of nine persons$, 8$ persons spent $Rs.\, 30$ each for their meals. The ninth one spent $Rs.\, 20$ more than the average expenditure of all the nine. The total money spent by all of them was (in $Rs.\,$)

The average weight of $36$ students is $50 \,kg$. If was found later that the weight of one of the student was misread as $73 \,kg$. whereas his actual weight was $37 \,kg$. Find the correct average. (in $kg$)

The average of nine numbers is $50.$ The average of the first five numbers is $54$ and that of the last three numbers is $52 .$ Then the sixth number is?

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 $n / m$ ?

A batsman in his $17^{th}$ innings, makes a score of $85$ runs, and there by, increases his average by $3$ runs. What is his average after the $17^{th}$ innings ? He had never been $'not out'.$