500 students sat for an examination in mathematics,physics and chemistry.45 passed all the three subject,60 passed mathematics and chemistry,70 passed physics and chemistry,50 passed mathematics and chemistry,10 passed in mathematics,80 passed in chemistry and 35 passed at least one subject. 1.how many student passed physics. 2.how many did not pass any subject.
To answer these questions, we can use a technique known as Venn diagrams, which use overlapping circles to represent different sets. Let's go step by step to find the answers:
Step 1: Determine the number of students passing at least one subject.
According to the information given, 35 students passed at least one subject.
Step 2: Fill in the Venn diagram with the given information.
We will use three overlapping circles representing mathematics (M), physics (P), and chemistry (C). We will fill in the information provided.
From the information given:
- 45 passed all three subjects (M, P, and C).
- 60 passed mathematics and chemistry (M and C).
- 70 passed physics and chemistry (P and C).
- 50 passed mathematics and chemistry (M and C).
- 10 passed mathematics only (M).
- 80 passed chemistry only (C).
- 35 passed at least one subject (M, P, or C).
Based on this information, the Venn diagram can be constructed as follows:
P
/ \
/ \
/ \
M-------C
Step 3: Calculate the number of students passing physics.
To find the number of students passing physics, we need to find the total number of students in the circle representing physics (P). From the information given, we know that 70 students passed physics and chemistry (P and C).
So, the number of students passing physics is 70.
Answer 1: The number of students passing physics is 70.
Step 4: Calculate the number of students who did not pass any subject.
To find the number of students who did not pass any subject, we need to find the number of students outside all three circles (M, P, and C).
From the information given, we can calculate this:
- 35 students passed at least one subject (M, P, or C) out of the total 500 students.
- So, the number of students who did not pass any subject is 500 - 35 = 465.
Answer 2: The number of students who did not pass any subject is 465.
In summary:
1. The number of students passing physics is 70.
2. The number of students who did not pass any subject is 465.