Question

2 POM
In a class of 50 students, 10 did not opt for math,
15 did not opt for science and 2 did not opt for
either. How many students of the class opted for
both math and science,
(a) 24
(b) 25
(c) 26
(d) 27​

Answer 1

d)27

Step-by-step explanation:

50 students total

10 did not opt for math

15 did not opt for science

2 did not opt for either

Total of 40 students in math and 13 did not opt for sci but did for math

40-13=27

27 students of the class opted for both math and science

Answer 2

$\huge{\boxed{\boxed{\mathfrak{\underline{\overline{\red{S{\green{o{\orange{l{\blue{u{\pink{t{\purple{i{\color{silver}o{\color{cyan}n}}}}}}}}}}}}}}}}}}}$

Let the no. of students opt for maths be n(M) and no. of students opt for science be n(S).

Given that Total no. of students in the class = 50

No. of students not opt for maths i.e., n(M') = 10, then n(M) = 50 - 10 = 40

No. of students not opt for science i.e., n(S') = 15, then n(S) = 50 - 15 = 35

No. of students not opt for both maths and science = 2

$\therefore$Total no. of students opted in the class = 50 - 2 = 48

Let it be n(U) = 48

We know the formula,

n(U) = n(A) + n(B) - n(A∩B)

Here A is M and B is S

$\therefore$ the formula for this sum is,

n(U) = n(M) + n(S) - n(M∩S)

48 = 40 + 35 - n(M∩S)

48 = 75 - n(M∩S)

n(M∩S) = 75 - 48

n(M∩S) = 27

$\therefore$ Option (d) 27 is the correct answer