Of the students at a certain high school, 40% take physics. Of those students who don’t take physics, 20% do take

Let percentages be as follows

\(a\%\) - Physics
\(b\%\) - Calculus
\(c\%\) - Both
\(d\%\) - None

Clearly, $$a\ +\ b\ +\ c\ +\ d\ =\ 100$$ $$a\ +\ c\ =\ 40$$ $$\left(b\ +\ d\right)\ =\ 100\ -\ \left(a\ +\ c\right)\ =\ 60$$ $$20\%\ \cdot\ \left(b\ +\ d\right)\ =\ b\ \ =12\%$$ $$d\ =\ 100\ -\ a\ -\ b\ -\ c\ =\ 100\ -\ \left(a\ +\ c\right)\ -\ b\ =\ 100\ -\ 40\ -\ 12\ =\ 48\%$$ C