In the first four examinations,each of $100$ marks,Ravi scored $94, 73, 72,$ and $84$ marks. If a final average greater than or equal to $80$ and less than $90$ is needed to obtain a final grade $'B'$ in a course,find the minimum marks that Ravi must obtain in the fifth examination to get grade $'B'$.

(77) Let the marks obtained by Ravi in the fifth examination be $x$.
The total marks for the five examinations are $94 + 73 + 72 + 84 + x = 323 + x$.
The average of the five examinations is $\frac{323 + x}{5}$.
According to the condition for grade $'B'$,the average must be at least $80$ and less than $90$:
$80 \le \frac{323 + x}{5} < 90$.
Multiplying the inequality by $5$:
$400 \le 323 + x < 450$.
Subtracting $323$ from all parts:
$400 - 323 \le x < 450 - 323$.
$77 \le x < 127$.
Since the maximum marks in an examination is $100$,the minimum marks required is $77$.