Why do these ask for the age and date of birth of the people living or staying in the household?

The data produced from this question is used in planning government programs that provide funding or services for specific age groups (e.g., school facilities planning, Head Start funding, services and assistance to seniors, including the Low Income Home Energy Assistance Program or LIHEAP). This data also facilitates the enforcement of laws against age discrimination. Both age and date of birth are asked to allow the Census Bureau to check for rounding errors and duplicate responses.