The average of marks obtained by $120$ candidates in a certain examination is $35 .$ If the average marks obtained by passed candidates are $39$ and those of the failed candidates are $15,$ then what is the number of candidates who passed the examination?

The average age of $20$ boys in the class is $15.6\, years.$ Five new boys join and the new average becomes $15.56\, years.$ What is the average age of the five new boys? (in $years$)

The average weight of $45$ students in a class is $52\, kg.$ Five of them whose average weight is $48 \,kg$ leave the class and other $5\, students$ whose average weight is $54\, kg$ join the class. What is the new average weight (in $kg$ ) of the class 

What is the average of all numbers between $100$ and $200$ which are divisible by $13\, ?$

A man spends $Rs.\,1800$ monthly on an average for the first four months and $Rs.\,2000$ monthly for the next eight months and saves $Rs.\,5600$ a $year$. His average monthly income is (in $Rs.$)

A student was asked to find the arithmetic mean of the numbers $3,11,7,9,15,13,8,19,17,21,14$ and $x$. He found the mean to be $12 .$ What should be the number in place of $x ?$