The average marks obtained by $100$ candidates in an examination are $45$. If the average marks of the passed students are $50$ while the average marks of the failed students is $40$. Then find the number of students who passed the examination.

An object travels $20$ meters in $4$ seconds and $15$ meters in the next two seconds. What is the average speed of the object?

$35$ is the average marks obtained by $120$ students. The average marks of successful candidates was $39$, and that of unsuccessful candidates was $15$. What is the number of successful candidates in that examination?

Average of three numbers $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ is $1$ more than the average of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. Average of $\mathrm{A}$ and $\mathrm{D}$ is $19.5$.

Quantity $1$: Find $\mathrm{A}$.

Quantity $2$: $21$.