NDA 2 2024 Maths, question 40

Topic: Algebra

Q40

In a class of $240$ students, $180$ passed in English, $130$ passed in Hindi and $150$ passed in Sanskrit. Further, $60$ passed in only one subject, $110$ passed in only two subjects and $10$ passed in none of the subjects. How many passed in all three subjects?

(a) $60$ Correct answer
(b) $55$
(c) $40$
(d) $35$

Solution.

Answer: (a) $60$

The number passing at least one subject is 240−10=230.
Of these, 60 passed exactly one and 110 exactly two, so 230−60−110=60 passed all three.
Check total subject passes: 60+2×110+3×60=460=180+130+150.