1. Tardigrade
  2. Question
  3. Mathematics
  4. 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 Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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.

WBJEEWBJEE 2012Sets

Solution:

According to question,
$a + b + c + d + e + f + g + h=100$ ...(i)
$h=1$ ...(ii)
$a + b + d +e=50$ ...(iii)
image
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 $d=2$