Question

10. An examination was taken by 500 students. There were three papers viz. Aptitude Reasoning and English. The number of students who passed in Aptitude, Reasoning and English are respectively 226 263 and 333. 106 students passed in both Aptitude and Reasoning, 152 students passed in both Reasoning and English while 142 students passed in both Aptitude and English. The number of students who passed only in English is 94. What is the difference in the number of students who passed in all the three subjects and the number of students who failed in all the three subjects?​

Answer 1

Answer:

please mark as brainlist

Answer 2

The difference is 32 students.

Given:

Total number of students = 500

Number of students who passed in Aptitude = 226

Number of students who passed in Reasoning = 263

Number of students who passed in English = 333

Number of students who passed in Aptitude and Reasoning = 106

Number of students who passed in Reasoning and English = 152

Number of students who passed in Aptitude and English = 142

To find: number of students who passed in all 3 subjects - number of students who passed in no subject

Solution:

Let students who passed in Aptitude = A

Let students who passed in Reasoning = R

Let students who passed in English = E

According to the question,

n(A) = 226

n(R) = 263

n(E) = 333

n(A∩R) = 106

n(R∩E) = 152

n(A∩E) = 142

Now,

number of students who passed only in English = 94

⇒ n(E) - n(E∩R) - n(A∩E) + n(A∩E∩R) = 94

⇒ 333 - 152 - 142 + n(A∩E∩R) = 94

⇒ 39 + n(A∩E∩R) = 94

⇒ n(A∩E∩R) = 94 - 39 = 55

⇒ Number of students who passed in all three subjects = 55

Now,

number of students who passed in at least one subject

= n(AUEUR)

= n(A) + n(E) + n(R) - n(A∩E) - n(E∩R) - n(A∩R) + n(A∩E∩R)

= 226 + 263 + 333 - 106 - 152 - 142 + 55

= 477

⇒ Number of students who failed all subjects = total students - 477

= 500 - 477

= 23

⇒ Number of students who failed all subjects = 23

⇒ Required difference = 55 - 23 = 32

∴ The difference is by 32 students.

SPJ2