2024 · Q98
In a class of 160 students, each of them opt at least one language from among English, Hindi and Sanskrit. It is found that 130 students opt English, 120 students Hindi and 110 Sanskrit. If the students opt either only one language or all three languages, then what is the number of students who study all three languages?
Elementary MathematicsSet Theory
- A40
- B60
- C80
- D100
Explanation
Let x be the number taking all three languages. Then only-English = 130−x, only-Hindi = 120−x, only-Sanskrit = 110−x (no one takes exactly two). Summing: (130−x)+(120−x)+(110−x)+x = 160, i.e. 360−2x = 160. Hence x = 100 — option D.