in an examination, 31 candidate passed chemistry, 29 passed physics and 3 failed both subject. if 50 candidate sat for the examination, how many of them passed chemistry only?
18 is the ans
To find out how many candidates passed chemistry only, we need to calculate the number of candidates who passed chemistry but did not pass physics.
We know that 31 candidates passed chemistry, 29 passed physics, and 3 failed both subjects. Let's use a Venn diagram to visualize the information:
C (Chemistry)
/ \
/ \
/ \
P (Physics)
From the given information, it is clear that there are candidates who passed both chemistry and physics, but we don't know how many. However, we do know that 3 candidates failed both subjects.
To find the number of candidates who passed chemistry only, we need to subtract the number of candidates who passed both subjects from the total number of candidates who passed chemistry.
Total candidates who passed chemistry = 31
Candidates who passed both chemistry and physics = Unknown (represented by "x")
Candidates who passed chemistry only = 31 - x
From the given information, we can form the equation:
Total candidates = Candidates who passed chemistry only + Candidates who passed physics only + Candidates who passed both subjects + Candidates who failed both subjects
50 = (31 - x) + (29 - x) + x + 3
Now, we can solve the equation to find the value of "x":
50 = 31 - x + 29 - x + x + 3
50 = 63 - x
x = 63 - 50
x = 13
Therefore, the number of candidates who passed both chemistry and physics is 13.
Finally, to find the number of candidates who passed chemistry only, we can substitute the value of "x" into the equation:
Candidates who passed chemistry only = 31 - 13 = 18
So, 18 candidates passed chemistry only.