In a housing society of 100 families, every family reads at least one of three newspapers A, B and C. 60 families read A, 50 read B and 45 read C, and 10 families read all three newspapers. How many families read exactly two of the newspapers?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 35
When the three newspaper totals are added, a family that reads one paper is counted once, a family that reads exactly two papers twice, and a family that reads all three papers three times.
Let \(x\) families read exactly one paper and \(y\) families exactly two papers; 10 read all three
Every family reads at least one paper: \(x+y+10=100\), so \(x+y=90\)
Sum of the totals: \(x+2y+3\times 10=60+50+45=155\), so \(x+2y=125\)
Subtracting: \(y=125-90=35\)
(Then \(x=90-35=55\) families read exactly one paper)
