Question:
% of students of a class took Statistics and 45% took Mathematics. If each student took Statistics or Mathematics and 40 took both, the total number of students in the class was:
% of students of a class took Statistics and 45% took Mathematics. If each student took Statistics or Mathematics and 40 took both, the total number of students in the class was:
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For two sets $A$ and $B$, $|A\cup B|=|A|+|B|-|A\cap B|$. If “everyone chose at least one,” then $|A\cup B|=N$.
Updated On: Aug 13, 2025
- 160
- 180
- 200
- 225
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The Correct Option is A
Solution and Explanation
Let the class size be $N$. Using inclusion–exclusion and the fact that everyone took at least one of the two subjects:
\[
N=\underbrace{0.80N}_{\text{Statistics}}+\underbrace{0.45N}_{\text{Mathematics}}-\underbrace{40}_{\text{both}}.
\]
So $N=1.25N-40$ which gives $0.25N=40$ and hence $N=160$.
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