The average weight of $21$ boys was recorded as $64 \,kg.$ If the weight of the teacher was added, the average increased by one $kg.$ What was the teacher's weight?

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 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?

$3 \,years$ 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 $year$.

Find the average of first $25$ multiples of $5 .$

In the first $10$ overs of a cricket game, the run rate was only $3.2 .$ What should be the run rate in the remaining $40$ overs to reach the target of $282$ runs ?