The family's monthly onion expenditure is Rs. 100 for the first three months and Rs. 50 for the next two months. Over the first five months, they purchase 10, 5, 4, 2, and 1 kilograms of onions, totaling 22 kilograms. The cumulative spending for this period is Rs. 400.
The average cost per kilogram of onions is calculated using the formula: \[ \text{Average Expense} = \frac{\text{Total Expenditure}}{\text{Total Amount Bought}} \] With the provided data: \[ \text{Average Expense} = \frac{400}{22} \approx 18 \, \text{rupees per kilogram}. \]
The average cost per kilogram is Rs. \( \boxed{18} \).