Directions: Study the given information carefully to answer the questions.

Out of 6500 students from the Art-wing of a college 21% of the total number of students have majored only in Psychology. 12% of the total number of students have majored only in English literature, 15% of the total number of students have majored only in Politics. 7% of the total number of students have majored only in Philosophy and 10% of the total number of students have majored only in History. 8% of the total number of students have majored in both Psychology as well as Philosophy. 4% of the total number of students have majored in History as well as Politics and 11% of the total number of students have majored in English literature as well as Politics. 9% of the total Number of students have majored in Psychology and English literature and 3% of the total number of students have majored in History and Philosophy.
Important for :
1
What is the respective ratio of the number of students majored in Philosophy to number of students majored only in Psychology?
» Explain it
C
As per the venn diagram,

Total % of students majored in Philosophy = (7 + 8 + 3)% = 18%

And

% of students majored only in Psychology = 21%

 Reqd ratio = 18% = 6 : 7 21%
2
Students majored in History are approximately, what per cent of the total number of students majored in Politics?
» Explain it
D
As per the venn diagram,

Total % of students majored in History = (10 + 4 + 3)% = 17%

And

Total % of students majored in politics = (15 + 4 + 11)% = 30%

 ∴   Reqd % = 17 × 100 = 56.66 %  ≈  57%. 30
3
How many students have majored only in Politics?
» Explain it
B
As per the venn diagram,

Therefore, No. of students majored only in Politics = 15% of 6500

= (10% + 5%) of 6500
= 650 + 325
= 975
4
What is the total number of students majored in English literature?
» Explain it
E
As per the venn diagram,

Total % of students majored in English = (12 + 9 + 11)% of 6500

= 32% of 6500
= (30% + 2%) of 6500
= 1950 + 130
= 2080
5
Lowest number of students have majored in which subject?
» Explain it
A
On adding all % values for different subjects,

we can observe that the lowest number of students has majored in History.