Vehicle ownership distribution – cars first, then motorcycles: In a locality of 80 families, 20% of the families own a car (one each). Of the remaining families, 50% own a motorcycle (one each). How many families do not own any vehicle?

Introduction / Context:This is a sequential-partition problem: first select car owners, then among the remainder select motorcycle owners. The groups are disjoint by construction (motorcycle selection happens after removing car-owning families).

Given Data / Assumptions:

• Total families = 80
• Car owners = 20% of 80 = 16
• Remaining families after cars = 80 − 16 = 64
• Motorcycle owners = 50% of remaining = 32

Concept / Approach:Add the two disjoint sets of vehicle owners and subtract from the total to get the count with no vehicle.

Step-by-Step Solution:Total with a vehicle = 16 + 32 = 48No-vehicle families = 80 − 48 = 32

Verification / Alternative check:Proportions check: 32/80 = 40% have no vehicles, consistent with the sequential selection.

Why Other Options Are Wrong:30 and 36 misapply percentages; 23 is unrelated to 80.

Common Pitfalls:Taking 50% of the original 80 instead of the remainder (64).

Final Answer:32