Let's draw the table for $5$ months:
$\begin{array}{|l||c|c|c|c|c|} \hline & 1^{\text{st}}\;\text{month} & 2^{\text{nd}}\;\text{month} & 3^{\text{rd}}\;\text{month} & 4^{\text{th}}\;\text{month} & 5^{\text{th}}\;\text{month} \\\hline \text{Onion sold} & \text{₹}\;10 & \text{₹}\;20 & \text{₹}\;25 & \text{₹}\;25 & \text{₹}\;50 \\ \text{(Rs./kg)} & & & & & \\\hline \text{Amount spend} & \text{₹}\;100 & \text{₹}100 & \text{₹}\;100 & \text{₹}\;50 & \text{₹}\;50 \\ \text{by family} & & & & & \\\hline \text{Weight} & 10\;\text{kg} & 5\;\text{kg} & 4\;\text{kg} & 2\;\text{kg} & 1\;\text{kg} \\\hline \end{array}$
Total amount spent by family $=\text{₹}\;400$
Total onion weight $=22\; \text{kg}$
$\therefore$ The average expense for onion, in rupees per kg, for the family over these $5$ months $= \dfrac{\text{₹}\;400}{22\;\text{kg}}$
$\qquad \qquad = \dfrac{200}{11} = 18.18 \cong 18\;\text{rupees/kg}.$
Correct Answer $:\text{A}$