A class has students where 72% took Biology and 44% took Mathematics. Each student took at least one of these subjects, and 40 students took both. What was the total number of students in the class?

Introduction / Context:
This is a classic inclusion–exclusion percentage problem. We are told the percentages of students taking Biology and Mathematics, that everyone took at least one, and that 40 students took both. The task is to recover the total class size from these data points.

Given Data / Assumptions:

• B% = 72% of total N took Biology.
• M% = 44% of total N took Mathematics.
• Both = 40 students.
• Every student took Biology or Mathematics (or both), so union = 100% of N.

Concept / Approach:
Use inclusion–exclusion: Biology + Mathematics − Both = Union. In percentage terms, 0.72N + 0.44N − Both = N. Solve this linear equation for N using the given Both = 40.

Step-by-Step Solution:

Verification / Alternative check:
Check counts: Biology = 0.72*250 = 180; Mathematics = 0.44*250 = 110; both = 40; union = 180 + 110 − 40 = 250, matching total N.

Why Other Options Are Wrong:
200, 240, and 320 do not satisfy 0.16N = 40. 180 is a distractor resembling Biology-only count, not the total.

Common Pitfalls:
Adding 72% and 44% to get 116% and assuming that equals the total, without subtracting the overlap. Always manage the double-counted intersection via inclusion–exclusion.

Final Answer:
250