Explanation
To find the number of students who passed in both subjects, we can use the principles of Set Theory.
1. Define the percentages:
Total students (n(U)) = 350
Passed in Mathematics (M) = 48%
Passed in Science (S) = 46%
Failed in both subjects = 38%
2. Calculate the percentage of students who passed at least one subject:
Since 38% failed in both subjects, the percentage of students who passed at least one subject (Mathematics or Science, which is the Union of M and S) is:
n(M∪S)=100%−38%=62%
3. Use the formula for the union of two sets:
The formula is:
n(M∪S)=n(M)+n(S)−n(M∩S)
Where n(M∩S) represents the students who passed in both subjects. Substituting the known values:
62%=48%+46%−n(M∩S)
62%=94%−n(M∩S)
n(M∩S)=94%−62%=32%
4. Calculate the total number of students:
Now, calculate 32% of the total number of students (350):
Number of students=350×10032
Number of students=3.5×32=112
Conclusion:
The number of students who passed in both subjects is 112. Therefore, the correct option is (c).
