There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.

Question

There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects. (A) is 12 (B) is 4 (C) is 2 (D) cannot be determined from the given information

Tardigrade Admin · Accepted Answer

According to question, a + b + c + d + e + f + g + h=100 ...(i) h=1 ...(ii) a + b + d +e=50 ...(iii) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/eb2835a63b162bc77bad95f79fd99b80-.png" /> Venn diagram shows failed students b + c + d +f=45 ...(iv) d + e + f +g=40 ...(v) b + e +f=32 ...(vi) On solving, the above equations, we get d=2

Q. There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.

is 12

is 4

is 2

cannot be determined from the given information

According to question, a+b+c+d+e+f+g+h=100 ...(i) h=1 ...(ii) a+b+d+e=50 ...(iii) Venn diagram shows failed students b+c+d+f=45 ...(iv) d+e+f+g=40 ...(v) b+e+f=32 ...(vi) On solving, the above equations, we get d=2

According to question,
$a + b + c + d + e + f + g + h = 100$ ...(i)
$h = 1$ ...(ii)
$a + b + d + e = 50$ ...(iii)

Venn diagram shows failed students
$b + c + d + f = 45$ ...(iv)
$d + e + f + g = 40$ ...(v)
$b + e + f = 32$ ...(vi)
On solving, the above equations, we get $d = 2$