The average marks of a group of $20$ students on a test is reduced by $4$ when the topper who scored $90$ marks is replaced of a new students. Find the marks of the new student.

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.

The average marks of $120$ students are $35.$ If average of passed students was $39$ and failed students was $15,$ then Find the number of students who have passed?

The mean of $100$ items was $46 .$ Later on it was discovered that an item $16$ was misread as $61$ and another item $43$ was misread as $34 .$ It was also found that the number of items twas $90$ and not $100 .$ Then what is the correct mean?

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 marks of $40$ students in an English exam is $72 .$ Later it is found that three marks $64 , 62$ and $84$ were wrongly entered as $68,65$ and $73.$ The average after mistakes were rectified is