In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is

(a) 10
(b) 9 ✓ UPSC's answer
(c) 5
(d) 4

Why the answer is (b)

• Total people = 15; those who read neither = 3, so those who read at least one language = 15 - 3 = 12.

• Let F = French readers = 7, E = English readers = 8.

• Using the inclusion-exclusion principle: |F ∪ E| = |F| + |E| - |F ∩ E|.

• Substituting values: 12 = 7 + 8 - |F ∩ E|, which gives |F ∩ E| = 3 (people who read both).

• People who read exactly one language = (Total reading at least one) - (People reading both) = 12 - 3 = 9.

• Therefore, the number of people who can read exactly one language is 9, corresponding to option (b).

Why the other options are wrong

(a) 10: 10 is not the count; exactly one language = only French (4) + only English (5) = 9.
(c) 5: 5 is only the number who read English alone (8 − 3); adding the 4 who read only French gives 9.
(d) 4: 4 is only the number who read French alone (7 − 3); adding the 5 who read only English gives 9.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.