In an examination of 2000 candidates, every candidate took Physics or Mathematics or both. If 65.8% took Physics and 59.2% took Mathematics, how many took both subjects?

Introduction / Context:Again, an inclusion–exclusion principle question, but this time we must convert the union (100%, since every candidate took at least one) into an absolute count for the intersection using given percentages and total candidates.

Given Data / Assumptions:Total candidates = 2000. Physics = 65.8%. Mathematics = 59.2%. Everyone took at least one.

Concept / Approach:Physics + Mathematics − Both = 100% of the candidates. Therefore, Both % = Physics % + Mathematics % − 100%. Multiply by total to get headcount.

Step-by-Step Solution:

Verification / Alternative check:Union check: 65.8 + 59.2 − 25 = 100%. Numbers balance perfectly.

Why Other Options Are Wrong:750, 250, 125, and 600 correspond to incorrect percentage conversions or misuse of inclusion–exclusion.

Common Pitfalls:Forgetting that the union equals 100% here, or miscomputing percentages of the total population.

Final Answer:500