In a class of 140 students, 16 students do not participate in any of the quiz and Ashu competitions. 70 students participate in the quiz and 77 students take part in the Ashu competition. How many students participate in both the quiz and Ashu competition activities?

In a class of 140 students, 16 students do not participate in any of the quiz and Ashu competitions. 70 students participate in the quiz and 77 students take part in the Ashu competition. How many students participate in both the quiz and Ashu competition activities? Correct Answer 23

Total student = 140

Students do not take part in any of the quiz and Ashu competitions = 16

Students who take part in Quiz and Ashu completion n(U) = 140 - 16 = 124

Students take part in Quiz n(Q) = 70

Students take part in Ashu competitions n(A) = 77

Students participate in both the quiz and Ashu competition = n(Q U A)

Now; 

n(QUA) = n(Q) + n(A) - n(Q∩A)

124 = 70 + 77 - (Q∩A)

(Q∩A) = 147 - 124

(Q∩A) = 23

Hence, Students participate in both the quiz and Ashu competition is 23.

Related Questions

The question below is followed by two statements I and II. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. Two friends Ashu and Manoj are running around from A to B simultaneously. Whenever Ashu reaches either end he runs back and continues at the same speed. Whenever Manoj meets Ashu he turns around and continues to run at the same speed, so when Ashu comes at A for the first time is how far from Manoj who is at B? I) The ratio of their speeds is 5 ∶ 3 and the track is of 800 m. II) Their speeds are equal.