Question

In an examination, every candidate took either Physics or Mathematics or both $84\%$ of the candidates took Physics and candidates who took Mathematics were half of those who took Physics. The total number of candidates being $1000$, how many took both Physics and Mathematics?

• A. $200$
• B. $240$
• C. $250$
• D. $260$

Answer 1

The correct option is D $260$

$n(P\cup M)=100\%,n\left(M\right)=42\%,n\left(P\right)=84\%$

$n(P\cap M)=n\left(M\right)+n\left(P\right)-n(P\cup M)$

= $42+84-100=26\%$

Number of Candidates who have taken both

= $\frac{26}{100}\times 1000=260$