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 of $6$ numbers is $20 .$ If one number is removed, the average becomes $15 .$ What is the number removed?

The average age of a class of $30$ students and a teacher reduce by $0.5 \,years$ if we exclude the teacher. If the initial average is $14 \,years,$ find the age of the class teacher in $year$ ?

The average speed of a train in the onward journey is $25\, \%$ less than that of the return journey, The train halts for one hour on reaching the destination. The total time taken for the complete to and fro journey is $17\, hours,$ covering a distance of $800 \,km$. The speed of the train in the onward journey is (in $km/h$)

The sum of three consecutive odd numbers is $38$ more than the average of these numbers. What is the first of these numbers