Question 44

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

Solution

Assume the number of students who failed in exactly 1 subject is x

The number of students who failed in exactly 2 subjects is y

The number of students who failed in exactly 3 subjects is z

Now, x+2y+3z=50+45+40=135

x+y+z=100-1=99

On subtracting the two equations, we get,

y+2z=36

It is given that y=32

Hence, 2z=36-32=4 =>z=2

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