Question

All the students of a batch opted Psychology, Business, or both. $73$% of the students opted Psychology and $62$% opted Business. If there are $220$ students, how many of them opted for both Psychology and business?

• A. $60$
• B. $100$
• C. $77$
• D. $35$

Answer 1

The correct option is C $77$

Let $P$ and $B$ the percentage of Students who opted Psycology an Business respectively.

Total Number of student$=220$

Total percentage of student$=100$

$P\cup B=P+B-P\cap B$

$P\cap B=P+B-P\cup B$

$=73+62-100=135-100=35$

Percentage of student who opted both students $=35\%$

Number of student who opted both subject$=\frac{220}{100}\times 35$

$=77$ students.