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Question:

In a city, 50% of the population can speak in exactly one language among Hindi, English and Tamil, while 40% of the population can speak in at least two of these three languages. Moreover, the number of people who cannot speak in any of these three languages is twice the number of people who can speak in all these three languages. If 52% of the population can speak in Hindi and 25% of the population can speak exactly in one language among English and Tamil, then the percentage of the population who can speak in Hindi and in exactly one more language among English and Tamil is

Explanation:

Let the number of people who speak

Exactly 3 languages = a
Exactly 2 languages = b
Exactly 1 language = c
No language = d

⇒ a + b + c + d = 100   ...(1)

Given, c = 50 and a + b = 40   ...(2)

From (1) and (2) we get, d = 10   ...(3)

The number of people who cannot speak in any of these three languages is twice the number of people who can speak in all these three languages
⇒ d = 2a​​​​​​​
∴ a = 5 [d = 10 from (3)]

Now, 52% of the population can speak in Hindi and 25% of the population can speak exactly in one language among English and Tamil. We can make the following Venn Diagram with the information so far.

​​​​​​​

Total orange region = 25

Now, Number of people speaking exactly one language (c) = 50 = (Only Hindi speaking people) + (Only English speaking people) + (Only Tamil speaking people)
⇒ 50 = (Only Hindi speaking people) + 25
⇒ Only Hindi speaking people = 25​​​​​​​

Also, Total Hindi speaking people = Only Hindi + (Hindi and exactly one other language) + (All three languages)
⇒ 52 = 25 + (Hindi and exactly one other language) + 5
⇒ Hindi and exactly one other language = 22

Hence, option (a).