JAMB 2004 · UME · Q10

Sets & Venn diagrams

In a class of 40 students, each student offers at least one of Physics and Chemistry. If the number that offer Physics is three times the number that offer both, and the number that offer Chemistry is twice the number that offer Physics, find the number of students that offer Physics only.

Worked solution (try it first)

Let $b$ offer both.
Then $3b$ offer Physics and $2 \times 3b = 6b$ offer Chemistry.
Everyone offers at least one, so $3b + 6b - b = 40$ , which gives $8b = 40$ and $b = 5$ .
Physics has $3 \times 5 = 15$ students, so Physics only is $15 - 5 = 10$ , option C.

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