Question

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Topic-Set theory​

Answer 1

ANSWER :

★ (c) 3 × 10⁷

• ✎ If in a state with a population of 75 × 10⁶, 45% of them know Hindi, 22% know English, 18% know Sanskrit, 12% know Hindi and English, 8% know English and Sanskrit, 10% know Hindi and Sanskrit and 5% know all the three languages; then the number of people who do not know any of the above three languages will be 3 × 10⁷.

___________________________________________________________

SOLUTION :

❒ Given :-

• Total population of the state = 75 × 10⁶.

• 45% of the population know Hindi.

• 22% of the population know English.

• 18% of the population know Sanskrit.

• 12% of the population know Hindi and English.

• 8% of the population know English and Sanskrit

• 10% of the population know Hindi and Sanskrit.

• 5% of the population know all the three languages.

❒ To Calculate :-

• The number of people who do not know any of the above three languages = ?

____________________________________________

❒ Calculation :-

Suppose,

In the Venn Diagram,

• E = Set of people who know English

• H = Set of people who know Hindi

• S = Set of people who know Sanskrit

So,

• E = 22%

• H = 45%

• S = 18%

• H ⋂ E = 12%

• E ⋂ S = 8%

• H ⋂ S = 10%

• E ⋂ H ⋂ S = 5%

From the Venn Diagram, we get,

• ✠ People who know English only = 22% - (7% + 5% + 3%)

➨ People who know English only = 22% - 15%

➨ People who know English only = 7%

Similarly,

• ✠ People who know Hindi only = 45% - (7% + 5% + 5%)

➨ People who know Hindi only = 45% - 17%

➨ People who know Hindi only = 28%

And,

• ✠ People who know Sanskrit only = 18% - (5% + 5% + 3%)

➨ People who know Sanskrit only = 18% - 13%

➨ People who know Sanskrit only = 5%

Thus,

• ⍟ People who know at least one language = 7% + 7% + 28% + 5% + 5% + 3% + 5%

➜ People who know at least one language = 60%

So,

• ⍟ People who donot know any language = 100% - 60%

➜ People who donot know any language = 40%

It means,

• 40% of the total population donot know any of the three languages.

Here,

• Total population of the state = 75 × 10⁶

• People who donot know any of the three languages = 40%

So,

• ✪ Number of people who donot know any of the three languages = 40% of Total Population

⇒ Number of people who donot know any of the three languages = 40% × (75 × 10⁶)

⇒ Number of people who donot know any of the three languages = $\sf{\dfrac{40}{100} \times 75 \times 10 {}^{6}}$

⇒ Number of people who donot know any of the three languages = 30 × 10⁶

∴ Number of people who donot know any of the three languages = 3 × 10⁷

Answer 2

Answer:

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The given pie Chart gives the marks scored in an examination by a student in English , Hindi , Science & Technology , Social Science and Mathematics.If the total marks obtained by the student were 540.The subject in which the student scored 105 marks , is ______ .

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Correct option is D)

Total Marks Obtained =540

Marks obtained in Mathematics =

360

90

×540=135

Marks obtained in Social Science =

360

65

×540=97.5

Marks obtained in Science & Technology =

360

80

×540=120

Marks obtained in Hindi =

360

70

×540=105

Marks obtained in English =

360

55

×540=82.5

The subject in which student scored 105 marks is Hindi.