The average of three consecutive odd numbers is $52$ more than $\frac{1}{3}$ of the largest of these numbers. What is the smallest of these numbers?

The average age of $5$ members is $21 \text{ years}$. If the age of the youngest member is $5 \text{ years}$,find out the average age of the family at the birth of the youngest member (in $\text{years}$).

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

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

The average of $6$ numbers is $8$. What is the $7^{th}$ number so that the average becomes $10$?

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?