Question

In a survey of population of $450$ people, it is found that $205$ can speak English, $210$ can speak Hindi and $120$ people can speak Tamil. If $100$ people can speak both Hindi and English; $80$ people can speak both English and Tamil, $35$ people can speak Hindi and Tamil and $20$ people can speak all the three languages, find the number of people who can speak English but not Hindi or Tamil.

• A. $40$
• B. $45$
• C. $50$
• D. $55$

Answer 1

Answer: (B)

$45$

Given, $N=450,n\left(H\right)=210,n\left(E\right)=205,n\left(T\right)=120$

$n(H\cap E)=100,n(E\cap T)=80,n(H\cap T)=35,n(H\cap E\cap T)=20$
From Venn diagram, we can write
$n(E\cap H^{\prime }\cap T^{\prime })=n\left(E\right)-n(E\cap H)-n(E\cap T)+n(E\cap H\cap T)$
$=205-100-80+20=45$