Question

In a class of 55 students, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is [UPSEAT 1990] (a) 6 (b) 9 (c) 7 (d) All of these

Answer 1

Given: 55 students in a class, the number of students studying different subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects.

To find:  The number of students who have taken exactly one subject?

Solution:

• Now we have given total student as : 55

• So let n(M) = student studying maths

                  n(C)=student studying chemistry

                  n(P)=student studying Physics

• So:

                  n(M) = 23, n(P) = 24, n(C) = 19, n(M∩P) = 12, n(M∩C) = 9 ,

                  n(P∩C) = 7, n(M∩P∩C) = 4

• So now, number of student who study maths but not physics and chemistry  are as follows:

                  n(M) − [ (n(M∩C) + n(M∩P) ] + n(M∩P∩C)

                  23 − [ 9 + 12 ] + 4  = 6

• Now, student study  chemistry but not physics and maths are as follows:

                  n(C)−[(n(M∩C)+n(P∩C)]+n(M∩P∩C)

                  19 − [ 9 + 7 ] + 4 = 7

• At last, student studying physics  but not maths  and chemistry  are as follows:

                  n(P) − [ ( n(M∩P) + n(P∩C) ] + n(M∩P∩C)

                  24 − [ 12 + 7 ] + 4 = 9

• So the students studying exact one subject are:

                  6 + 7 + 9 = 22

Answer:

          So the students studying exact one subject are 22.