The average weight of $25$ persons is increased by $1 \, kg$ when one man weighing $60 \, kg$ is replaced by a new person. What is the weight of the new person (in $kg$)?

The average of $3$ numbers is $22$. If the first number is $\frac{3}{8}$ of the sum of the other two numbers,what is the first number?

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

Average rainfall on Monday,Tuesday,Wednesday and Thursday is $420.5\, cm$ and average on Tuesday,Wednesday,Thursday and Friday is $440.5\, cm$. If the ratio of rainfall for Monday and Friday is $20:21$,find the rainfall in $cm$ on Monday and Friday.

Of three numbers,the second is thrice the first and the third number is three-fourths of the first. If the average of the three numbers is $114$,the largest number is

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 was $90$ and not $100$. Then,what is the correct mean?