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In a gathering on 100 people, 70 of them can speak Hindi, 60 can speak English and 30 can speak French. Further, 30 of them can speak both Hindi and English, 20 can speak both Hindi and French. If x is the number of people who can speak both English and French, then which one of the following is correct? (Assume that everyone can speak at least one of the three languages.)

In a gathering on 100 people, 70 of them can speak Hindi, 60 can speak English and 30 can speak French. Further, 30 of them can speak both Hindi and English, 20 can speak both Hindi and French. If x is the number of people who can speak both English and French, then which one of the following is correct? (Assume that everyone can speak at least one of the three languages.) Correct Answer 9 < × ≤ 30

Let the number of people who speak all three languages be y

Total number of people = ∑Number of people speaking English, French and Hindi – ∑Number of people speaking two languages + Number of people speaking three languages

⇒ 100 = 70 + 60 + 30 – 30 – 20 – x + y

⇒ 100 = 110 – x + y

⇒ x = 10 + y

⇒ Least possible value of y = 0,

⇒ x ≥ 10

y cannot exceed 20, because for knowing all three languages, they should know Hindi and French too, only 20 people know Hindi and French

If y = 20

then x ≤ 30

∴ 10 ≤ × ≤ 30 or 9 < × ≤ 30

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