In a group of 1000 people, each can speak either Hindi or English. There are 750 people who can speak Hindi and 400 who can speak English.Then number of persons who can speak Hindi only is
 

$$\begin{gathered} n\left(P\right)=1000,n\left(H\right)=750,n\left(B\right)=400 \\ n\left(P\right)=n(H\cup B) \\ n\left(P\right)=n\left(H\right)+n\left(B\right)-n(H\cap B) \\ \Rightarrow 1000=750+400-\mathrm{n}(\mathrm{H}\cap \mathrm{B}) \\ \Rightarrow \mathrm{n}(\mathrm{H}\cap \mathrm{B})=1150-1000 \\ =150 \\ \text{ Hence, }150\text{ people can speak both Hindi and Bengali nowH }=(H-B)\cup (H\cap B)\text{, } \\ \therefore \mathrm{n}\left(\mathrm{H}\right)=\mathrm{n}(\mathrm{H}-\mathrm{B})+\mathrm{n}(\mathrm{H}\cap \mathrm{B}) \\ \Rightarrow 750=n(H-B)+150 \\ \Rightarrow \mathrm{n}(\mathrm{H}-\mathrm{B})=750-150 \\ =600 \end{gathered}$$