Question

From the information given, answer the following question
1) A painter knows Hindi.
2) A farmer, an advocate and a teacher can speak English fluently.
3) Except for the teacher, the other three know Gujarati.
4) Out of Marathi and Hindi, the advocate and the farmer speak only Marathi, but the teacher can speak both languages.
Who knows Marathi as well as Gujarati?
A) Painter and the advocate
B) The farmer and the teacher
C) The advocate and the farmer
D) The teacher and the painter

Answer 1

Hint:
We can consider people who know each language as a set. Then we can add elements to the sets by reading the given information one by one. Then we can take the intersection of the two sets that we need to find. Then the elements in the intersection will be the required answer.

Complete step by step solution:
Let H be the set of people who knows Hindi,
 E be the set of people who knows English
G be the set of people who knows Gujarati and
M be the set of people who know Marathi.
Now we can add elements to the set from the given information.
It is given that the painter knows Hindi. So we can add the painter to the set H.
$ \Rightarrow H = \left\{ {{\text{painter}}} \right\}$
Then it is given that a farmer, an advocate and a teacher can speak English fluently. So, we can add them to the set E.
\[ \Rightarrow E = \left\{ {{\text{advocate,teacher,farmer}}} \right\}\]
It is given except for the teacher, the other three know Gujarati. So we can add them to G.
\[ \Rightarrow G = \left\{ {{\text{advocate, painter, farmer}}} \right\}\]
Then we have, out of Marathi and Hindi, the advocate and the farmer speak only Marathi, but the teacher can speak both languages. So, we can add all of them to set M and the teacher to set H.
\[ \Rightarrow M = \left\{ {{\text{advocate, teacher, farmer}}} \right\}\]
\[ \Rightarrow H = \left\{ {{\text{painter, teacher}}} \right\}\].
Now we need to find people who know both Marathi and Gujarati. So, we can take their intersection. We know that intersection of 2 sets gives the elements that contained in both the sets.
\[ \Rightarrow M \cap G = \left\{ {{\text{advocate, farmer}}} \right\}\]
As the intersection contains only the advocate and the farmer, only they know both Marathi and Gujarati.

So, the correct answer is option C which is the advocate and the farmer.

Note:
Alternate method to solve this problem is by eliminating the options,
Consider option A, Painter and advocate.
From condition (4), only the farmer, advocate and teacher know Marathi. As painters don’t know Marathi, option A can be rejected.
Consider B, farmer and teacher.
It is clear from condition 3 that the teacher doesn't know Guajarati. So, B can’t be the answer.
Consider option C, advocate and farmer.
From conditions (3) and (4), we can say that both of them know both Marathi and Gujarati.
So, option C can be the correct answer.
Consider option D, farmer and teacher.
It is clear from condition 3 that the teacher doesn't know Guajarati. So, D can’t be the answer.
Therefore, the correct answer is option C which is the advocate and the farmer.