In a survey of 50 newspaper readers, 40 read Champion and 30 read Guardian, how many read both papers?

Analyze the question: 50 people read newspapers. 40 read Champion and 30 read Guardian. We need the number who read both.

Concept: This is a two-set Venn diagram problem. The key formula is:

n(C ∪ G) = n(C) + n(G) − n(C ∩ G)

The question says the 50 are all "newspaper readers", so every person reads at least one paper. That means n(C ∪ G) = 50.

Solution:

50 = 40 + 30 − n(C ∩ G)

50 = 70 − n(C ∩ G)

n(C ∩ G) = 70 − 50 = 20

Check:

• Champion only = 40 − 20 = 20
• Guardian only = 30 − 20 = 10
• Both = 20
• Total = 20 + 10 + 20 = 50 ✓

Answer: 20 readers read both papers, which is option D.

Tip: When every person in the group belongs to at least one set (no one is "neither"), use: Both = n(A) + n(B) − Total. If the question mentions people who read neither, subtract them from the total first.