Sets and Venn Logic – English-only speakers from group totals: In a group of 50 people, 35 speak Hindi, 25 speak both Hindi and English, and every person speaks at least one of Hindi or English. How many people speak only English (i.e., English but not Hindi)?

Introduction / Context:
This question tests basic inclusion-exclusion on two overlapping sets (Hindi speakers and English speakers). We are asked for the count of people who speak only English given totals and overlap, with the assurance that everyone speaks at least one language.

Given Data / Assumptions:

• Total group = 50
• Hindi speakers H = 35
• Both languages (H ∩ E) = 25
• Every person speaks at least one of Hindi or English (no outsiders)

Concept / Approach:
For two sets, |H ∪ E| = |H| + |E| − |H ∩ E|. Here |H ∪ E| = 50. Solve for |E|, then subtract the overlap to get English-only.

Step-by-Step Solution:
50 = 35 + |E| − 25|E| = 50 − 35 + 25 = 40English-only = |E| − |H ∩ E| = 40 − 25 = 15

Verification / Alternative check:
Compute Hindi-only: 35 − 25 = 10. Then 10 (Hindi-only) + 15 (English-only) + 25 (both) = 50 (consistent).

Why Other Options Are Wrong:
10 is Hindi-only; 20 and 40 conflict with inclusion-exclusion constraints.

Common Pitfalls:
Subtracting the overlap from the total directly or mixing up Hindi-only with English-only.

Final Answer:
15