Discussion

Explanation:

Let number of people who can speak
Exactly one of the three languages = a
Exactly one of the three languages = b
Exactly one of the three languages = c
None of the three languages = n

⇒ a + b + c + n = 100   …(1)

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

Now, we need to minimize a. 

Let’s see if a can be 0.
From (1), if a = 0 and even if b = 100 and c = 0
a + 2b + 3c = 200

But we want this sum to be 180 [from (2)].

So we will have to reduce the value of b and increase the value of the variable with smaller coefficient i.e., a.

Now, if even decrease b by 1 unit and increase a by 1 unit.
a + 2b + 3c = 199 i.e., the sum decreases by 1 unit.

∴ To decrease the sum from 200 to 180, we need to decrease it by 20 units, hence we need to transfer 20 units from b to a.

∴ Least possible value of a = 20.

Following is a possible Venn diagram for this case.

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Hence, 20.

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