In an examination, 25 candidates passed physics and 27 candidates passed further maths, 10 candidates passed both subjects and 5 candidates failed both subjects. Find the number of candidates that
i. Passed only physics
ii. Passed furthermaths only
iii. Sat for the exam
Venn Diagram
i) 25-10=15
ii) 27-10=17
25+27-10 = 42 passed something, so
iii) 42+5 = 47 sat the exam
To find the number of candidates who passed only physics, we need to subtract the number of candidates who passed both subjects from the total number of candidates who passed physics.
1. Passed only physics = Passed physics - Passed both subjects
Passed only physics = 25 - 10 = 15
Therefore, 15 candidates passed only physics.
To find the number of candidates who passed further maths only, we need to subtract the number of candidates who passed both subjects from the total number of candidates who passed further maths.
2. Passed further maths only = Passed further maths - Passed both subjects
Passed further maths only = 27 - 10 = 17
Therefore, 17 candidates passed further maths only.
To find the total number of candidates who sat for the exam, we need to add the number of candidates who passed physics only, passed further maths only, passed both subjects, and failed both subjects.
3. Total candidates = Passed only physics + Passed only further maths + Passed both subjects + Failed both subjects
Total candidates = 15 + 17 + 10 + 5 = 47
Therefore, 47 candidates sat for the exam.