Question

Out of 50 students in a class,10 student like maths but not science and 15 students like science but not maths.if 10 students like neither of both subjects find the ratio of the students who like maths or science

Answer 1

The number of students who like math and science can be calculated as follows:

Total number of students who like math or science = Total number of students who like math + Total number of students who like science - Total number of students who like both

Total number of students who like math or science = 10 + 15 - (50 - 10 - 15 - x) = 25 - (25 - x) = x

where x is the number of students who like both math and science.

Since there are 10 students who like neither subject, the total number of students who like math or science is:

x + 10

The ratio of students who like math or science is:

(x + 10) / 50

We do not have enough information to determine the value of x, so we cannot calculate the ratio of students who like math or science.

Answer 2

Let's denote:

M: the set of students who like maths

S: the set of students who like science

n(M): the number of students who like maths

n(S): the number of students who like science

n(M ∩ S): the number of students who like both maths and science

n(M ∪ S): the number of students who like maths or science (or both)

We can use the principle of inclusion-exclusion to find n(M ∪ S):

n(M ∪ S) = n(M) + n(S) - n(M ∩ S)

From the problem statement, we know:

n(M) = 10

n(S) = 15

n(M ∩ S) = ? (unknown)

We also know that 10 students like neither maths nor science, which means that:

n(M ∪ S)' = 10

where (M ∪ S)' denotes the complement of M ∪ S, i.e., the set of students who do not like maths or science.

We can use the formula:

n(A') = N - n(A)

where N is the total number of students (N = 50).

n(M ∪ S)' = n((M ∪ S))' = N - n(M ∪ S) = N - (n(M) + n(S) - n(M ∩ S))

Substituting the known values:

n((M ∪ S))' = 50 - (10 + 15 - n(M ∩ S)) = 25 + n(M ∩ S)

Simplifying:

n(M ∩ S) = n((M ∪ S))' - 25 = 10

Therefore, we have:

n(M ∪ S) = n(M) + n(S) - n(M ∩ S) = 10 + 15 - 10 = 15

The ratio of the students who like maths or science is:

n(M ∪ S) / N = 15 / 50 = 3/10

So the required ratio is 3:10.

Explanation: