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?

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 of marks obtained by $150$ candidates in a certain examination is $50 .$ If the average marks of passed candidates is $55$ and that of the failed candidates is $25,$ what is the number of candidates who passed the examination?

A cricketer gives $12.4$ runs per wicket. He gives $26$ runs and takes $5$ wicket in a match after which his average becomes $12$ per wicket. How many wickets had been taken till the last match?

$3 \,years$ 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 $year$.