Question

In a group of 100 persons, 80 people can speak Malayalam and 60 can speak English. Then the number of people who speak English only is

• A. 40
• B. 30
• C. 20
• D. 25
• E. 35

Hint:

Venn Diagram Tip: English only = Total English speakers minus people who speak both languages.

Answer 1

The Correct Option is C

Concept:
Use the inclusion-exclusion principle: $$n(M \cup E)=n(M)+n(E)-n(M \cap E)$$ where $M$ = Malayalam speakers and $E$ = English speakers.

Step 1: Substitute given values.
Total persons = 100 Malayalam speakers: $$n(M)=80$$ English speakers: $$n(E)=60$$ Assuming everyone speaks at least one language: $$n(M \cup E)=100$$

Step 2: Find common speakers.
Using formula: $$100=80+60-n(M \cap E)$$

Step 3: Solve for intersection.
$$100=140-n(M \cap E)$$ $$n(M \cap E)=40$$

Step 4: Find English only speakers.
English only means: $$n(E)-n(M \cap E)$$ So: $$60-40=20$$

Step 5: Select the answer.
Therefore, the number of people who speak English only is: $$20$$ Hence the correct answer is (C) 20.