Class size from percentages with a known overlap (both subjects): In a class, 72% took Biology and 44% took Mathematics. Each student took at least one of these subjects, and 40 students took both. Find the total number of students in the class.

Introduction / Context:Percentages of two overlapping groups sum to more than 100% due to the overlap. When the numeric overlap is given, we can solve for the total by equating inclusion-exclusion to the class size.

Given Data / Assumptions:

• Let total = N
• Biology = 0.72N
• Mathematics = 0.44N
• Both = 40
• At least one → union size = N

Concept / Approach:Inclusion-exclusion for counts: |B ∪ M| = |B| + |M| − |B ∩ M|. Here |B ∪ M| = N, and |B ∩ M| = 40.

Step-by-Step Solution:N = 0.72N + 0.44N − 40N − 1.16N = −40 → −0.16N = −40 → N = 250

Verification / Alternative check:Both percentage = 0.72 + 0.44 − 1 = 0.16 → 0.16N = 40 → N = 250 (same).

Why Other Options Are Wrong:200, 240, 320 do not satisfy 0.16N = 40.

Common Pitfalls:Forgetting that the union equals the whole class when each student takes at least one subject.

Final Answer:250