In a survey, 80% owned a car and 60% owned a mobile phone. If 55% owned both, what percentage owned a car or a mobile phone or both?

Introduction / Context:
An inclusion–exclusion application in percentage form: find the union of two ownership sets (car, phone) given each set’s size and their intersection. This is a standard survey analysis question.

Given Data / Assumptions:
Car = 80%, Phone = 60%, Both = 55%. We assume all percentages are of the same surveyed population.

Concept / Approach:
Union % = Car % + Phone % − Both %. Subtract the intersection once to correct for double counting of those who own both items.

Step-by-Step Solution:

Verification / Alternative check:
If 85% own at least one, then 15% own neither. This is plausible and consistent with the given overlap of 55%.

Why Other Options Are Wrong:
65% and 80% underestimate by failing to add both sets properly. 97.5% is unrelated to inclusion–exclusion here. 90% overcounts the overlap.

Common Pitfalls:
Adding without subtracting the intersection or subtracting the intersection twice. Always use the formula A + B − A∩B.

Final Answer:
85%