Q156
ReasoningVenn Diagrams & Set Theory
The result of a survey of 1000 persons with respect to their knowledge of Hindi (H), English (E) and Sanskrit (S) is given in a Venn diagram (with region values 200, 120, 220, 100, 80, 110, 170 as shown). What is the ratio of those who know all three languages to those who do not know Sanskrit?
- a.$\dfrac{1}{9}$
- b.$\dfrac{1}{10}$
- c.$\dfrac{10}{17}$
- d.$\dfrac{5}{27}$
Answer: (D) $\dfrac{5}{27}$
From the diagram, 100 people know all three languages. Those who do not know Sanskrit at all are those in the Hindi-only, English-only, and Hindi-and-English-only regions: $200+220+120 = 540$. So the required ratio is $\dfrac{100}{540} = \dfrac{5}{27}$.