Question

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,


24
25
26
27

​

Answer 1

Step-by-step explanation:

10 did not opt for math means 40 opt for math.

15 did not opt for science means 35 opt for science.

2 did not opt for both means 8 opt for science but not maths & 13 did not opt for science but for maths.

So required ans is 27 opt for both.

Ans C.

Answer 2

27 students opted for both math and science.

Given:

Total students in the class (T) = 50

Number of students that did not opt for science (A') = 15

Number of students that did not opt for math (B') = 10

Number of students that did not opt for anything (T') = 2

To find:

Number of students that opted for both math and science (A∩B).

Explanation:

It is given total students in the class as 50,

Also given that 10 did not opt for math which means 50 - 10 = 40 students opted for math (A).

Similarly,

50-15 =35 students opted for science (B).

Also, we have that 2 students did not opt for anything,

Therefore, these students should be kept out of nominal roll for academics.

Which means total students becomes 50-2 =48 (T).

Now,

We know an equation,

T = n(A) + n(B) - n(A∩B)

Substituting the above values, we get

48 = 40 + 35 - n(A∩B)

48 = 75 - n(A∩B)  ; or

n(A∩B) = 27

Final answer:

Hence, the number of students that opted for both math and science is option (d) 27.