In a class of 150 students the following result were obtained in a certain examination , 45 students failed in Maths , 50 students failed in physics ,48 students failed in chemistry , 30 students failed in both Maths and physics ,32 failed in physics and chemistry , 35 failed in both Maths and chemistry ,25 in all the three subject.Draw a venn diagram and Find the number of students who have failed in at least one subject .
Answers
Answer:
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Answer:
Given that there are 100 students and only one student passed in all 3 subjects
So the number of students failed in at least one subject is 99
Let a be the number of students failed only in mathematics, b be number of students failed only in physics and c be number of students failed only in Biology.
Let x be number of students failed only in mathematics and physics, y be number of students failed only in physics and biology and z be the number of students failed only in biology and mathematics.
Let p be the number of students failed in all three subjects
By Venn diagram, we get 99=a+b+c+x+y+z+p
Number of students failed in exactly two subjects is 32=x+y+z
Students failed in mathematics is 50=a+x+z+p , students failed in physics is 45=b+x+y+p and students failed in Biology is 40=c+y+z+p
By adding above three equations, we get 135=a+b+c+2(x+y+z)+3p
⇒135=99+32+2p
⇒p=2
Therefore option C is correct