In a survey of 200 students of a school, it was found that 60% study mathematics, 45% study

physics, 35% study chemistry, 20% study mathematics and physics, 15% study physics and
chemistry, 25% study chemistry and mathematics and 10% none of these subjects. Find the
number of students who study all the three subjects using Venn diagrams only.

so, did you draw your diagram? Just start filling in the spaces.

answer => 40

200=120+90+70-40-30-50+X
=> X=200-160 = 40

Answer is 20 because 10% means 20 student are those which are not studying any subject.

To find the number of students who study all three subjects using Venn diagrams, we can follow these steps:

1. Draw three overlapping circles to represent the subjects: mathematics, physics, and chemistry.

2. Use the given information to fill in the known percentages of students who study each subject. Start by filling in the percentages that involve only one subject.

- 60% study mathematics
- 45% study physics
- 35% study chemistry

3. Fill in the percentages that involve two subjects. For example:
- 20% study both mathematics and physics
- 15% study both physics and chemistry
- 25% study both chemistry and mathematics

To fill in the overlap regions, subtract the percentages that involve only one subject from the percentages that involve two subjects.

- For the overlap between mathematics and physics: 20% - 60% = -40% (ignore negative values)
- For the overlap between physics and chemistry: 15% - 45% = -30% (ignore negative values)
- For the overlap between chemistry and mathematics: 25% - 35% = -10% (ignore negative values)

4. Since we have 10% of students who study none of these subjects, subtract this value from the total number of students.

5. Add up the percentages in the overlapping regions, including the ones we subtracted in Step 3, to get the percentage of students who study all three subjects.

6. Convert the percentage to the actual number of students by multiplying it by the total number of students in the survey (200).

By following these steps, you should be able to determine the number of students who study all three subjects using Venn diagrams.