The average of marks obtained by $100$ candidates in a certain examination is $30 .$ If the average marks of passed candidates is $35$ and that of the failed candidates is $10,$ what is the number of candidates who passed the examination?

The average income of $A$ for $15$ days is $Rs.\,70.$ The average for first five days is $Rs.\, 60$ and that for the last nine days is $Rs.\,80.$ A's income for the sixth day is (in $Rs.\,$ )

The average of six numbers is $32 .$ If each of the first three numbers is increased by $2$ and each of the remaining three numbers is decreased by $4,$ then the new average is ?

The average weight of all the $11$ players of Indian cricket team is $50\, kg.$ If the average of first six lightest weight players is $49\, kg$ and that of the six heaviest players is $52\, kg$. The average weight of the player which lies in the sixth position in the list of players when all the $11$ $players$ are arranged in the order of $increasing$ or $decreasing$ $weights$ (in $kg$)

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