If $72$ persons build a $220\text{-m-long}$ wall in $6$ days, then how many persons will be required to build the same type of wall of $550\text{-m}$ length in $5$ days?

We can use the Work-Manpower-Days relationship formula:
$$\frac{M_1\times D_1}{W_1}=\frac{M_2\times D_2}{W_2}$$
Where:$M_1=72$, $D_1=6$, $W_1=220$$M_2=?$, $D_2=5$, $W_2=550$ Substitute the values:
$$\frac{72\times 6}{220}=\frac{M_2\times 5}{550}$$
Simplify the denominators by dividing both sides by $110$:
$$\frac{72\times 6}{2}=\frac{M_2\times 5}{5}$$
Simplifying further:
$$36\times 6=M_2\times 1$$
$$M_2=216$$
Thus, $216$ persons are required.