Question : In an examination every candidate took science or civics or both. 65.8% took science and 59.2% took civics. If the total number of candidates was 2000, how many took both?
— question on set theory, out of forty students, there are ,triple venn diagram worksheet, union formula for 3 sets,—
Solution:
Science = 65.8%
Civics= 59.2%
Total candidates = 2000
Both Subject Candidates = ?
We know the formula;
Science subject candidates + Civics subject candidates – Both subject candidates = Total candidates
\[ 65.8%+59.2%-Both subject candidates %= 100% \]
\[ Both subject candidates %age = 65.8%+59.2%-100% \]
\[ ==> Both subject candidates %age = 125%-100%=25% \]
\[ ==> Both subject candidates %age= 25% \]
So, 25% out of 2000 candidates opt for both the subjects;
\[ so, 25% of 2000 = \frac{25}{100} \times 2000 \]
\[ = 500 \]
So, 500 candidates took both science and civics