Here, we have,

Suppose, the total number of people be n (P) = 950

The people who can speak English n (E) = 460

The people who can speak Hindi n (H) = 750

(i) How many people can speak both Hindi and English.

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

As we know,

n (P) = n (E) + n (H) – n (H ∩ E)

By 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 people can speak Hindi only.

As 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

∴ 490 people can speak only Hindi.

(iii) How many people can speak English only.

As 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) = 460 – 260 = 200

Hence, 200 people can speak only English.