Question

In a class, $54$ students are good in Hindi only, $63$ students are good in Mathematics only and $41$ students are good in English only. There are $18$ students who are good in both Hindi and Mathematics. $10$ students are good in all three subjects. What is the number of students who are good in Hindi and Mathematics but not in English?

• A. $18$
• B. $12$
• C. $10$
• D. $8$

Answer 1

The correct option is D $8$

This is a question of venn diagram

No. of students who are good in either Hindi or Mathematics but not in English

$=54+18+63$

$=125$

Let $H_1{M}_1{E}_1$ denote the set of students studying Hindi,

Mathematics and English.

No. of students of English only $=41$

No. of students of Hindi only $=63$

No. of students of Maths only $=54$

$n(H\cap M\cap E)=10$

$n(H\cap M)=18$

No. of students who study ${}^{\prime }{H}^{\prime }$ or ${}^{\prime }{M}^{\prime }$ but not ${}^{\prime }{E}^{\prime }$

$=63+54+18=125$.

No of students who age good in Hindi and Mathematics but not in English $=18-10$

$=8$.