Question

Out of 15 persons 10 can speak Hindi and 8 can speak English.How many persons can Speak Hindi only.

• A. $7$
• B. $4$
• C. $2$
• D. None

Answer 1

Answer: (A)

$7$

$\begin{array}{c}n\left(H\right)=10\\ n\left(E\right)=8\\ n(H\cup E)=n\left(H\right)+n\left(E\right)+n(H\cap E)\\ 15=n\left(H\right)+n(E\cap H)+n\left(E\right)+n(E\cap H)-n(E\cap H)\\ n(E\cap H)=3\end{array}$

Total persons speaking Hindi $=10$

$\begin{array}{cc}\text{Person speaKing only Hindi}& =n\left(H\right)-n(E\cap H)\\ & =10-3\\ & =7\end{array}$

, (A) is the correct option