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

The average of marks obtained by $150$ candidates in a certain examination is $50 .$ If the average marks of passed candidates is $55$ and that of the failed candidates is $25,$ what is the number of candidates who passed the examination?

$16$ children are to be divided into two groups $A$ and $B$ of $10$ and $6$ children, respectively. The average marks obtained by the children of group $A$ is $75$ and that of all the children is $76 .$ Then, the average marks of the children of group $B$ is ?

The average age of a cricket team reduces by $2$ when two senior players aged $32$ and $30$ are replaced by $2$ youngsters of equal age. What is the age of these players?

The average of $8$ numbers is $20 .$ The average of first two numbers is $15 \frac{1}{2}$ and that of next three is $21 \frac{1}{3}$. If the sixth number is less than the seventh and eighth numbers by $4$ and $7$ respectively, then the eighth number is

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