Question

Among a number of students in a class 25 read physics, 13 read chemistry and 28 read maths .If 12 read both Physics and Chemistry, 15 read chemistry and maths and 18 read Physics and mathematics and 10 read all the three subjects. Find the number of students?​

Answer 1

ANSWER :

• ❖ If among a number of students in a class 25 read physics, 13 read chemistry and 28 read maths, 12 read both Physics and Chemistry, 15 read chemistry and maths and 18 read Physics and mathematics and 10 read all the three subjects; then the total number of students is 31.

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SOLUTION :

Let's assume that,

• P = Set of students who read Physics

• C = Set of students who read Chemistry

• M = Set of students who read Maths

Then,

• P ⋂ C = Set of students who read both Physics and Chemistry

• C ⋂ M = Set of students who read both Chemistry and Maths

• P ⋂ M = Set of students who read both Physics and Maths

• P ⋂ C ⋂ M = Set of students who read all the three subjects

• P U C U M = Set of total students

❒ Given :-

• n (P) = 25

• n (C) = 13

• n (M) = 28

• n (P ⋂ C) = 12

• n (C ⋂ M) = 15

• n (P ⋂ M) = 18

• n (P ⋂ C ⋂ M) = 10

❒ To Find :-

• n (P U C U M) = ?

❒ Formula :-

• n (P U C U M) = n (P) + n (C) + n (M) - n (P ⋂ C) - n (C ⋂ M) - n (P ⋂ M) + n (P ⋂ C ⋂ M)

❒ Calculation :-

Substituting the values in the formula we get,

• n (P U C U M) = n (P) + n (C) + n (M) - n (P ⋂ C) - n (C ⋂ M) - n (P ⋂ M) + n (P ⋂ C ⋂ M)

➜ n (P U C U M) = 25 + 13 + 28 - 12 - 15 - 18 + 10

➜ n (P U C U M) = 76 - 45

n (P U C U M) = 31 ★

• ✎ Total number of students is 31.