In a college library, four different business newspapers - Economic Times,…
2024
In a college library, four different business newspapers - Economic Times, Business Standard, Business Line and Financial Express - are available. All students visit the library regularly, but 20% of them do not read any business newspaper. The four newspapers, in the order given above, are read by 230, 180, 180 and 220 students respectively. The number of students reading exactly 2 newspapers, for any pair of two newspapers, is 20. There are 30 students who read all four newspapers, but nobody reads exactly three out of the four newspapers.
What percentage of the people reading Business Standard also read at least one other newspaper?
- A.
250%
- B.
100%
- C.
50%
- D.
150%
Attempted by 6 students.
Show answer & explanation
Correct answer: C
Concept: For a population split across 4 categories, when data is given as 'exactly-k-categories' counts (exactly 2, exactly 3, exactly 4), each person is counted once in every category they belong to. So the sum of the four individual category totals equals 1×(exactly-1 total) + 2×(exactly-2 total) + 3×(exactly-3 total) + 4×(exactly-4 total). This identity lets you recover the 'only-this-category' count for any one category once its overlap contributions (the exactly-2, exactly-3, exactly-4 groups that include it) are known.
Sum of the four readerships = 230 + 180 + 180 + 220 = 810.
There are 6 possible pairs of newspapers; each pair has exactly 20 students reading only that pair, so the exactly-2 total (all pairs combined) = 6 × 20 = 120.
Exactly-3 total = 0 (given). Exactly-4 total = 30 (given).
Apply the identity: 810 = (exactly-1 total) + 2(120) + 3(0) + 4(30) = (exactly-1 total) + 240 + 120, so exactly-1 total = 810 − 360 = 450 students read exactly one newspaper (across all four papers).
Now isolate Business Standard's own split. Of the 6 pairs, 3 involve Business Standard (Business Standard–Economic Times, Business Standard–Business Line, Business Standard–Financial Express), contributing 3 × 20 = 60 students who read Business Standard and exactly one other paper. The all-four group (30) also reads Business Standard. Exactly-3 involving Business Standard = 0.
So Business Standard readers who read at least one other newspaper = 60 + 0 + 30 = 90.
Required percentage = (90 / 180) × 100 = 50%.
Cross-check: As a consistency check, total unique newspaper readers = exactly-1 (450) + exactly-2 (120) + exactly-3 (0) + exactly-4 (30) = 600. Since 20% of students read no newspaper at all, these 600 readers form 80% of all students, giving 600 / 0.8 = 750 students in total — a clean whole number that confirms the arithmetic above is internally consistent.