Let , Total number of people be n(P) = 950

People who can speak English n(E) = 460

People who can speak Hindi n(H) = 750

i. How many can speak both Hindi and English.

People who can speak both Hindi and English = n (H ∩ E)

We know,

n (P) = n(E) + n(H) – n (H ∩ E)

Substituting the values we get

950 = 460+750 – n (H ∩ E)

950= 1210 – n (H ∩ E)

n (H ∩ E)=260.

Number of people who can speak both English and Hindi are 260.

ii. How many can speak Hindi only.

We can see that H is disjoint union of n(H–E) and n (H ∩ E).

(If A and B are disjoint then n (A ∪ B) = n(A) + n(B))

∴ H = n(H–E) ∪ n (H ∩ E).

⇒ n(H) = n(H–E) + n (H ∩ E).

⇒ 750 = n (H – E)+ 260

⇒ n(H–E) = 490.

Only, 490 people speak Hindi.

iii. how many can speak English only.

We can see that E is disjoint union of n(E–H) and n (H ∩ E).

(If A and B are disjoint then n (A ∪ B) = n(A) + n(B))

∴ E = n(E–H) ∪ n (H ∩ E).

⇒ n(E) = n(E–H) + n (H ∩ E).

⇒ 460 = n (H – E)+ 260

⇒ n(H–E) = 200.

Only, 200 people speak English.