Question

in an examination 120 students passed intergrated science or mathematics. if 30 passed both subjects and 18 more passed mathematics than intergrated science, fin the number of candidates who passed in each subject

Answer 1

To solve the exam problem, we used the principle of inclusion-exclusion to form equations and solve for the number of students who passed Integrated Science (66) and Mathematics (84).

Step-by-step explanation:

In an examination, 120 students passed Integrated Science or Mathematics. Out of these, 30 passed both subjects. It is also given that 18 more students passed Mathematics than Integrated Science.

To find out the number of students who passed each subject, we can use the principle of inclusion-exclusion for sets.

Let M be the number of students who passed Mathematics and S be the number who passed Integrated Science. We have the following equations stemming from the problem statement:

1. M + S - 30 = 120 (since the 30 students who passed both are counted twice)
2. M = S + 18 (since 18 more students passed Mathematics)

Substituting equation (2) into equation (1), we get:

S + 18 + S - 30 = 120

2S - 12 = 120

2S = 132

S = 66

Now that we know S, we can solve for M:

M = S + 18 = 66 + 18 = 84

Therefore, 66 students passed Integrated Science, and 84 students passed Mathematics.