In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% took Mathematics. The total number of candidates was 2000. How many candidates took both Physics and Mathematics ?

Use the inclusion–exclusion principle: |P ∪ M| = |P| + |M| − |P ∩ M|. Since every candidate took at least one subject, |P ∪ M| = 100%. The problem gives Physics = 65.8%, Mathematics = 59.2%, and total candidates = 2000. Applying the formula (written also in set/percentage form) yields |P ∩ M|% = 65.8% + 59.2% − 100% = 25.0%. Converting to counts: 25.0% of 2000 = 0.25 × 2000 = 500. Therefore 500 candidates took both Physics and Mathematics, so option 2 is correct.