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?

A cyclist goes from a place to another and returns by the same route. He pedals his way uniformly with speed $u$ while going and with speed $v$ while returning. The average speed of his journey is

The average marks obtained by $180$ students in an examination is $50 .$ If the average marks of passed students is $40 .$ Then what is the number of students who failed the examination ?

The average of marks obtained by $120$ candidates was $35.$ If the average of marks of passed candidates was $39$ and that of failed candidates was $15,$ the number of candidates who passed the examination is

A group of boys has an average weight of $36 \,kg$. One boy weighing $42 \,kg$ leaves the group and another boy weighing $30\, kg$ joints the group. If the average now becomes $35.7\, kg$, then how many boys are there in the group?

The average of three consecutive odd numbers is $12$ more than one-third of the first of these numbers. What is the last of the three numbers ?