Bissoy.com
Doctors Medicines MCQs Q&A

In a class of 50 students, 30 take Mathematics, 25 take Biology and 15 take both Mathematics and Biology. How many students take neither Mathematics nor Biology?

In a class of 50 students, 30 take Mathematics, 25 take Biology and 15 take both Mathematics and Biology. How many students take neither Mathematics nor Biology? Correct Answer 10

Given:

The total number of students in a class = 50 

The number of students takes Mathematics = 30

The number of students takes Biology = 25

The number of students take both Mathematics and Biology = 15

Formula used:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B) 

n(A ∪ B)' = n(U) - n(A ∪ B)

where, n(A) = number of elements in A, n(B) = number of elements in B

n(A ∩ B) = number of elements in both A and B, n(A ∪ B) = number of elements in either A or B

n(U) = number of total students

Calculation:

Let the set of total students be U, the set of students takes Mathematics be A

And the set of students takes Biology be C.

According to the question,

n(U) = 50, n(A) = 30, n(B) = 25 and n(A ∩ B) = 15

Now, students take either Mathematics or Biology = n(A ∪ B)

⇒ n(A) + n(B) - n(A ∩ B) 

⇒ 30 + 25 - 15

⇒ 40

So, students take neither Mathematics nor Biology = n(A ∪ B)'

⇒ n(U) - n(A ∪ B)

⇒ 50 - 40

⇒ 10

∴ The students take neither Mathematics nor Biology is 10.

Related Questions

In a junior college with 500 students, 250 students study Mathematics, and 200 students study Biology. One hundred students study neither Mathematics nor Biology. How many students study both Mathematics and Biology?
Among 80 students, 24 passed in Chemistry, 35 passed in Physics and 29 passed in Mathematics, 8 students did not appear for the examination. If 2 students have passed in all the three subjects, 2 students have passed in Physics and Chemistry both but not in Mathematics, 2 students have passed in Chemistry and Mathematics both but not in Physics, and 8 students have passed in Physics and Mathematics both but not in Chemistry, then how many students have passed in Mathematics only?
Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. What is the average weight of new students added? I. In a class 60% students are male and there average weight is 15 kg more than the female students, 9 males and 6 new female students joined the class and the average weight of the class increased by 0.84 II. Total male students in the class is 12 more than female students adding 9 male students to the class increases the average weight of male students by 1 kg and adding 6 female students increases the average weight of female students by 0.6.
In a mid-term exam of class 11, 42% students failed in Mathematics, 54% students failed in Physics and 48% students failed in Chemistry. Only 10% students failed in all the three subjects. 20% students failed in both Physics and Chemistry, 15% students failed in both Chemistry and Mathematics, and 18% students failed in both Physics and Mathematics. What is the percentage of those students who failed in two subjects only?
In a competitive examination, 250 students have registered. Out of these, 50 students have registered for Physics, 75 students for Mathematics and 35 students for both Mathematics and Physics. What is the number of students who have registered neither for Physics nor for Mathematics?
In a group of 450 students, 22% of the total students take the Hindi subject, 34% of the total students take the Physics subject, and 26% of the total students take the Social Science subject. 8% of the total students have taken both Hindi and Physics subject only. Out of the total students in the Hindi subject, 1/3 have taken both Hindi and Social Science subject only. Out of the total students in the Physics subject, 1/3 have taken both Physics and Social Science subject only. Only 20 students take all the three subjects. Find the number of students who have not taken any subject.  
Read the data given below and answer the questions based on it. In the CBSE Board exams last year, 53% passed in Biology, 61% percent passed in English, 60% in Social studies, 24% in Biology and English, 35% in English and social studies, 27% in Biology and social studies and 5% in none. What is the ratio of percentage of students who passed in Biology and Social Studies but not English in relation to the percentage of students who passed in Social Studies and English but not Biology?
Carefully read the given information and answer the questions as per the following. 6 students Anil, Sita, Mansi, Kajal, Govind and Varu sit around looking around the center of a circular table (not necessarily in the same order). All six students prefer different subjects such as mathematics, physics, history, geography, chemistry and biology. i) The mathematics that likes it sits between the Kajal and the mansi. ii) The person who likes Chemistry is at the third position on the right side of Kajal. iii) Varun, who is not a neighbor of Govind, likes biology. iv) Kajal sits immediately on the left side of Varun. v) Govind does not like mathematics. vi) Sita is at the third position on the right side of the person who likes history. vii) Who likes physics and who like biology are neighbors. Who sits right between Varun and Sita?
Carefully read the given information and answer the questions as per the following. 6 students Anil, Sita, Mansi, Kajal, Govind and Varu sit around looking around the center of a circular table (not necessarily in the same order). All six students prefer different subjects such as mathematics, physics, history, geography, chemistry and biology. i) The mathematics that likes it sits between the Kajal and the mansi. ii) The person who likes Chemistry is at the third position on the right side of Kajal. iii) Varu, who is not a neighbor of Govind, likes biology. iv) Kajal sits immediately on the left side of Varu. v) Govind does not like mathematics. vi) Sita is at the third position on the right side of the person who likes history. vii) Who likes physics and who like biology are neighbors. Who likes history?
Carefully read the given information and answer the questions as per the following. 6 students Anil, Sita, Mansi, Kajal, Govind and Varu sit around looking around the center of a circular table (not necessarily in the same order). All six students prefer different subjects such as mathematics, physics, history, geography, chemistry and biology. i) The mathematics that likes it sits between the Kajal and the mansi. ii) The person who likes Chemistry is at the third position on the right side of Kajal. iii) Varu, who is not a neighbor of Govind, likes biology. iv) Kajal sits immediately on the left side of Varu. v) Govind like mathematics. vi) Sita is at the third position on the right side of the person who likes history. vii) Who likes physics and who like biology are neighbours. Which of the following statements is correct in relation to the system?