Question

31 candidates appeared for an examination, 15 candidates passed in Mathematics, 15 candidates passed in physics, 20 candidates passed in Chemistry, 3 candidates passed only in Mathematics, 4 candidates passed only in Physics. 7 candidates candidates passed only in Chemistry. 2 candidates passed in all the three subjects. How many candidates passed only in two subjects? a) 17 b) 15 c) 22 d) 14

Answer 1

Answer:

15 candidates

Step-by-step explanation:

Total candidates=31

Candidates passed only in Maths=3

Candidates passed only in Chem=7

Candidates passed only in Phy=4

Candidates passing only in 1 subject=7+3+4=14

Passing in all three=2

Therefore, passing in only 2 subjects=31-2-14=15

Here you can make a circle representing maths, and two other circles representing Phy, and Chemistry. These circles will intersect each other. That common intersection will contain 2 students. Then you can figure out the above solutions with respect to these circles.

Answer 2

Answer:

Number of candidates passed in only two subject is 15

option (b) is correct

Step-by-step explanation:

I have solved this problem by venn diagram method

Let M, P and C be the set of candidates passed in Mathematics, Physics and chemistry respectively.

From the given data, it is clear that all candidates are passed atlest one subject.

From the venn diagram, it is clear that

x+y+z is the total number of candidates passed in only two subjects.

n(M)=15

⇒3+2+x+z=15

⇒x+z=15-5

⇒x+z=10...........(1)

n(P)=15

⇒2+4+x+y=15

⇒x+y=15-6

⇒x+y=9...........(2)

n(C)=20

⇒2+7+y+z=20

⇒y+z=20-9

⇒y+z=11.........(3)

Adding (1), (2), (3) we get

2(x+y+z)=10+9+11

2(x+y+z)=30

x+y+z=15