**In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer ne...**

### Question

In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither Mathematics nor Physics. How many offer both Mathematics and Physics?

### Options

A) 4

B) 8

C) 16

D) 20

The correct answer is D.

### Explanation:

No of students in class = 40

(M) No of students who offer mathematics = 32 - x

(P) No of students who offer physics = 24 - x

(N) No of students who offer neither mathematics nor physics = 4

(B) No of student who offer both = x

Total no of students = M + P + N + B

40 = 32 - x + 24 - x + 4 + x

40 = 32 + 24 + 4 - x

40 = 60 - x

x = 60 - 40

x = 20

(M) No of students who offer mathematics = 32 - x

(P) No of students who offer physics = 24 - x

(N) No of students who offer neither mathematics nor physics = 4

(B) No of student who offer both = x

Total no of students = M + P + N + B

40 = 32 - x + 24 - x + 4 + x

40 = 32 + 24 + 4 - x

40 = 60 - x

x = 60 - 40

x = 20

Explanation provided by Mariam

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No of students in class = 40

(M) No of students who offer mathematics = 32 - x

(P) No of students who offer physics = 24 - x

(N) No of students who offer neither mathematics nor physics = 4

(B) No of student who offer both = x

Total no of students = M + P + N + B

40 = 32 - x + 24 - x + 4 + x

40 = 32 + 24 + 4 - x

40 = 60 - x

x = 60 - 40

x = 20

No. of students in class = 40

No. of students who offer Mathematics = 32

No. of students who offer Physics = 24

No. of students who offer neither Mathematics nor Physics = 4

No, of students who offer both Mathematics and Physics = x

32 + 24 + 4 - x = 40

x = 56 + 4 - 40 = 20