Discussion

Explanation:

Let the number of people speaking exactly one language = a
Let the number of people speaking exactly two languages = b
Let the number of people speaking exactly three languages = c
Let the number of people speaking none of the three languages = n

⇒ a + b + c + n = 100   …(1)

Also, a + 2b + 3c = 65 + 55 + 60
⇒ a + 2b + 3c = 180   …(2)

(2) – (1)
⇒ b + 2c – n = 80   …(3)

Number of people speaking at aleast one language = a + b + c
To mimise the number of people speaking at least one language we need to minimize a + b + c.

Since 65 people speak Hindi, a + b + c cannot be less than 65.

Hence, 65.

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